Relevant bibliographies by topics / Lie Groups, Harmonic and Fourier Analysis

Academic literature on the topic 'Lie Groups, Harmonic and Fourier Analysis'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Lie Groups, Harmonic and Fourier Analysis.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Lie Groups, Harmonic and Fourier Analysis"

1

Celeghini, Enrico, Manuel Gadella, and Mariano del Olmo. "Hermite Functions, Lie Groups and Fourier Analysis." Entropy 20, no. 11 (October 23, 2018): 816. http://dx.doi.org/10.3390/e20110816.

Full text
Abstract:
In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R + , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This can be done in terms of a unified framework based on the use of rigged Hilbert spaces. We find a relation between the universal enveloping algebra of the symmetry groups with the fractional Fourier transform. The results obtained are relevant in quantum mechanics as well as in signal processing as Fourier analysis has a close relation with signal filters. In addition, we introduce some new results concerning a discretized Fourier transform on the circle. We introduce new functions on the circle constructed with the use of Hermite functions with interesting properties under Fourier transformations.
APA, Harvard, Vancouver, ISO, and other styles
2

Barbaresco, Frédéric, and Jean-Pierre Gazeau. "Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century." Entropy 21, no. 3 (March 6, 2019): 250. http://dx.doi.org/10.3390/e21030250.

Full text
Abstract:
For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.
APA, Harvard, Vancouver, ISO, and other styles
3

Sarkar, Rudra P., and Alladi Sitaram. "The Helgason Fourier transform for semisimple Lie groups I: The Case of SL2(ℝ)." Bulletin of the Australian Mathematical Society 73, no. 3 (June 2006): 413–32. http://dx.doi.org/10.1017/s0004972700035437.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Liao, Ming. "Lévy processes and Fourier analysis on compact Lie groups." Annals of Probability 32, no. 2 (April 2004): 1553–73. http://dx.doi.org/10.1214/009117904000000306.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Donley, Robert W. "Orthogonality Relations and Harmonic Forms for Semisimple Lie Groups." Journal of Functional Analysis 170, no. 1 (January 2000): 141–60. http://dx.doi.org/10.1006/jfan.1999.3511.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Lin, Ying-Fen, Jean Ludwig, and Carine Molitor-Braun. "Nilpotent Lie Groups: Fourier Inversion and Prime Ideals." Journal of Fourier Analysis and Applications 25, no. 2 (December 1, 2017): 345–76. http://dx.doi.org/10.1007/s00041-017-9586-y.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Giulini, Saverio, and Giancarlo Travaglini. "Central Fourier analysis for Lorentz spaces on compact Lie groups." Monatshefte f�r Mathematik 107, no. 3 (September 1989): 207–15. http://dx.doi.org/10.1007/bf01300344.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Tricot, C. "AN INTRODUCTION TO HARMONIC ANALYSIS ON SEMI-SIMPLE LIE GROUPS." Bulletin of the London Mathematical Society 23, no. 2 (March 1991): 204–8. http://dx.doi.org/10.1112/blms/23.2.204.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Yang, Jae-Hyun. "Harmonic analysis on the quotient spaces of Heisenberg groups." Nagoya Mathematical Journal 123 (September 1991): 103–17. http://dx.doi.org/10.1017/s0027763000003676.

Full text
Abstract:
A certain nilpotent Lie group plays an important role in the study of the foundations of quantum mechanics ([Wey]) and of the theory of theta series (see [C], [I] and [Wei]). This work shows how theta series are applied to decompose the natural unitary representation of a Heisenberg group.
APA, Harvard, Vancouver, ISO, and other styles
10

Yang, Dilian. "Functional Equations and Fourier Analysis." Canadian Mathematical Bulletin 56, no. 1 (March 1, 2013): 218–24. http://dx.doi.org/10.4153/cmb-2011-136-7.

Full text
Abstract:
AbstractBy exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation-on compact groups.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Lie Groups, Harmonic and Fourier Analysis"

1

Li, Jialun. "Harmonic analysis of stationary measures." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0311/document.

Full text
Abstract:
Soit μ une mesure de probabilité borélienne sur SL m+1 (R) tel que le sous-groupe engendré par le support de μ est Zariski dense. Soit V une représentation irréductible de dimension finie de SL m+1 (R). D’après un théorème de Furstenberg, il existe une unique mesure μ-stationnaire sur PV et nous nous somme intéressés à la décroissance de Fourier de cette mesure. Le résultat principal de cette thèse est que la transformée de Fourier de la mesure stationnaire a une décroissance polynomiale. À partir de ce résultat, nous obtenons un trou spectral de l’opérateur de transfert, dont les propriétés nous permettent d’établir un terme d’erreur exponentiel pour le théorème de renouvellement dans le cadre des produits de matrices aléatoires. L’ingrédient essentiel est une propriété de décroissance de Fourier des convolutions multiplicatives de mesures sur R n , qui est une généralisation d’un théorème de Bourgain en dimension 1. Nous établissons cet ingrédient en utilisant un estimée somme produit de He et de Saxcé.Dans la dernière partie, nous généralisons un résultat de Lax et Phillips et un résultat de Hamenstädt sur la finitude des petites valeurs propres de l’opérateur de Laplace sur les variétés hyperboliques géométriquement finies
Let μ be a Borel probability measure on SL m+1 (R), whose support generates a Zariski dense subgroup. Let V be a finite dimensional irreducible linear representation of SL m+1 (R). A theorem of Furstenberg says that there exists a unique μ-stationary probability measure on PV and we are interested in the Fourier decay of the stationary measure. The main result of the thesis is that the Fourier transform of the stationary measure has a power decay. From this result, we obtain a spectral gap of the transfer operator, whose properties allow us to establish an exponential error term for the renewal theorem in the context of products of random matrices. A key technical ingredient for the proof is a Fourier decay of multiplicative convolutions of measures on R n , which is a generalisation of Bourgain’s theorem on dimension 1. We establish this result by using a sum-product estimate due to He-de Saxcé. In the last part, we generalize a result of Lax-Phillips and a result of Hamenstädt on the finiteness of small eigenvalues of the Laplace operator on geometrically finite hyperbolic manifolds
APA, Harvard, Vancouver, ISO, and other styles
2

Chung, Kin Hoong School of Mathematics UNSW. "Compact Group Actions and Harmonic Analysis." Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17639.

Full text
Abstract:
A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L (???g), along with a quadruple (s, E, j, E#), where s is a ???# - invariant, open neighbourhood of 0 in L G/L H, E is a test-function subspace of C??? (Exp s), j ?? C??? (s), and E# is a test-function subspace of C??? (s) which contains { j.f Exp: f ?? E }. Of interest is the question: Is the function ???: ?? ??? ????, where ??: f ??? j.f Exp, a local associative algebra homomorphism from F# with multiplication defined via convolution with respect to a function e: s x s ??? C, to F, with the usual convolution for its multiplication (where F is the space of all ??? - invariant distributions of E and F# is the space of all ???# - invariant distributions of E#)? For this system of objects, we can show that, to some extent, the choice of the function j is not critical, for it can be ???absorbed??? into the function e. Also, when K is compact, we can show that ??? ker ?? = { f ?? E : ???k f (???g) dg = 0}. These results turn out to be very useful for calculations on s2 ??? G/H, where G = SO(3) and H??? SO(3) with H ??? SO(2) with ??? : h ??? Lh, as we can use these results to show that there is no quadruple (s, E, j, E#) for SO(3)/H with j analytic in some neighbourhood of 0 such that ??? is a local homomorphism from F# to F. Moreover, we can show that there is more than one solution for the case where s, E and E# are as chosen by Rouviere, if e is does not have to satisfy e(??,??) = e(??,??).
APA, Harvard, Vancouver, ISO, and other styles
3

Wang, Simeng. "Some problems in harmonic analysis on quantum groups." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2062/document.

Full text
Abstract:
Cette thèse étudie quelques problèmes d’analyse harmonique sur les groupes quantiques compacts. Elle consiste en trois parties. La première partie présente la théorie Lp élémentaire des transformées de Fourier, les convolutions et les multiplicateurs sur les groupes quantiques compacts, y compris la théorie de Hausdorff-Young et les inégalités de Young.Dans la seconde partie, nous caractérisons les opérateurs de convolution positifs sur un groupe quantique fini qui envoient Lp dans L2, et donnons aussi quelques constructions sur les groupes quantiques compacts infinis. La méthode pour étudier les états non-dégénérés fournit une formule générale pour calculer les états idempotents associés aux images deHopf, qui généralise un travail de Banica, Franz et Skalski. La troisième partie est consacrée à l’étude des ensembles de Sidon, des ensembles _(p) et des notions associées pour les groupes quantiques compacts. Nous établissons différentes caractérisations des ensembles de Sidon, et en particulier nous démontrons que tout ensemble de Sidon est un ensemble de Sidon fort au sens de Picardello. Nous donnons quelques liens entre les ensembles de Sidon, les ensembles _(p) et les lacunarités pour les multiplicateurs de Fourier sur Lp, généralisant un travail de Blendek et Michali˘cek. Nous démontrons aussi l’existence des ensembles de type _(p) pour les systèmes orthogonaux dans les espaces Lp non commutatifs, et déduisons les propriétés correspondantes pour les groupes quantiques compacts. Nous considérons aussi les ensembles de Sidon centraux, et nous prouvons que les groupes quantiques compacts ayant les mêmes règles de fusion et les mêmes fonctions de dimension ont des ensemble de Sidon centraux identiques. Quelques exemples sont aussi étudiés dans cette thèse. Les travaux présentés dans cette thèse se basent sur deux articles de l’auteur. Le premier s’intitule “Lp-improving convolution operators on finite quantum groups” et a été accepté pour publication dans Indiana University Mathematics Journal, et le deuxième est un travail intitulé “Lacunary Fourier series for compact quantum groups” et a été publié en ligne dans Communications in Mathematical Physics
This thesis studies some problems in the theory of harmonic analysis on compact quantum groups. It consists of three parts. The first part presents some elementary Lp theory of Fourier transforms, convolutions and multipliers on compact quantum groups, including the Hausdorff-Young theory and Young’s inequalities. In the second part, we characterize positive convolution operators on a finite quantum group G which are Lp-improving, and also give some constructions on infinite compact quantum groups. The methods for ondegeneratestates yield a general formula for computing idempotent states associated to Hopf images, which generalizes earlier work of Banica, Franz and Skalski. The third part is devoted to the study of Sidon sets, _(p)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, _(p)-sets and lacunarities for Lp-Fourier multipliers, generalizing a previous work by Blendek and Michali˘cek. We also prove the existence of _(p)-sets for orthogonal systems in noncommutative Lp-spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included. The thesis is principally based on two works by the author, entitled “Lp-improvingconvolution operators on finite quantum groups” and “Lacunary Fourier series for compact quantum groups”, which have been accepted for publication in Indiana University Mathematics Journal and Communications in Mathematical Physics respectively
APA, Harvard, Vancouver, ISO, and other styles
4

Ebert, Svend. "Wavelets on Lie groups and homogeneous spaces." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2011. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-78988.

Full text
Abstract:
Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.
APA, Harvard, Vancouver, ISO, and other styles
5

Wang, Xumin. "Functional and harmonic analysis of noncommutative Lp spaces associated to compact quantum groups." Thesis, Bourgogne Franche-Comté, 2019. http://www.theses.fr/2019UBFCD040.

Full text
Abstract:
Cette thèse a pour but d'étudier l'analyse sur les groupes quantiques compacts. Elle se compose de deux parties. La première présente la classification des semi-groupes de Markov invariants sur ces espaces homogènes quantiques. Les générateurs de ces semi-groupes sont considérés comme des opérateurs de Laplace sur ces espaces.La sphère classique , la sphère libre et la sphère semi-libérée sont considérées comme des exemples et les générateurs de semi-groupes de Markov sur ces sphères sont classés. Nous calculons aussi les dimensions spectrales des trois familles de sphères en fonction du comportement asymptotique des valeurs propres de leur opérateur de Laplace.Dans la deuxième partie, nous étudions la convergence des séries de Fourier pour les groupes non abéliens et les groupes quantiques. Il est bien connu qu'un certain nombre de propriétés d'approximation de groupes peuvent être interprétées comme des méthodes de sommation et de convergence moyenne de séries de Fourier non commutatives associées. Nous établissons un critère général d'inégalités maximales pour les identités approximatives de multiplicateurs non commutatifs de Fourier. En conséquence, nous prouvons que pour tout groupe dénombrable discret moyennable, il existe une suite de fonctions définies positives à support fini, telle que les multiplicateurs de Fourier associés sur les espaces Lp non commutatifs satisfassent à la convergence ponctuelle. Nos résultats s'appliquent également à la convergence presque partout des séries de Fourier de fonctions Lp sur des groupes compacts non-abéliens. D'autre part, nous obtenons des bornes indépendantes de la dimension pour les inégalités maximales de Hardy-Littlewood non commutatives dans l'espace à valeurs opérateurs associées à des corps convexes
This thesis is devoted to studying the analysis on compact quantum groups. It consists of two parts. First part presents the classification of invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators on these spaces.The classical sphere, the free sphere, and the half-liberated sphere are considered as examples and the generators of Markov semigroups on these spheres are classified. We compute spectral dimensions for the three families of spheres based on the asymptotic behavior of the eigenvalues of their Laplace operator.In the second part, we study of convergence of Fourier series for non-abelian groups and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as some summation methods and mean convergence of associated noncommutative Fourier series. We establish a general criterion of maximal inequalities for approximative identities of noncommutative Fourier multipliers. As a result, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions, so that the associated Fourier multipliers on noncommutative Lp-spaces satisfy the pointwise convergence. Our results also apply to the almost everywhere convergence of Fourier series of Lp-functions on non-abelian compact groups. On the other hand, we obtain the dimension free bounds of noncommutative Hardy-Littlewood maximal inequalities in the operator-valued Lp space associated with convex bodies
APA, Harvard, Vancouver, ISO, and other styles
6

Avetisyan, Zhirayr. "Mode decomposition and Fourier analysis of physical fields in homogeneous cosmology." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-107907.

Full text
Abstract:
In this work the methods of mode decomposition and Fourier analysis of quantum fields on curved spacetimes previously available mainly for the scalar fields on Friedman-Robertson-Walker spacetimes are extended to arbitrary vector fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. Explicit constructions are performed for a variety of situations arising in homogeneous cosmology. A number of results concerning classical and quantum fields known for very restricted situations are generalized to cover almost all cosmological models.
APA, Harvard, Vancouver, ISO, and other styles
7

Silva, Fabiano Borges da. "Aplicações harmonicas e martingales em variedades." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306288.

Full text
Abstract:
Orientador: Paulo Regis Caron Ruffino
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-04T03:35:11Z (GMT). No. of bitstreams: 1 Silva_FabianoBorgesda_M.pdf: 388532 bytes, checksum: 847fc3b7dce8c11700ac92aff1ce3c34 (MD5) Previous issue date: 2005
Resumo: Este trabalho tem por finalidade explorar resultados de aplicacoes harmonicas, atraves do calculo estocastico em variedades. Esta organizado da seguinte forma: Nos dois primeiros capitulos sao introduzidos conceitos e resultados sobre calculo estocastico no Rn, geometria diferencial e grupos de Lie. No terceiro capitulo temos as definicoes de aplicacoes harmonicas e a equacao de Euler-Lagrange. E finalmente, no ultimo, damos uma caracterizacao para aplicacoes harmonicas atraves de martingales, que sera importante para explorar alguns resultados sobre aplicacoes harmonicas do ponto de vista do calculo estocastico em variedades
Abstract: In this work we explore results of harmonic mappings, via stochastic calculus in manifolds. The text is organized as follows: In the first two chapters, we introduce concepts and results about stochastic calculus in Rn, differential geometry and Lie groups. In the third chapter we have the definitions of harmonic mappings and the Euler-Lagrange equation. Finally, in the last chapter, we give a characterization of harmonic mappings via martingales, this will be important to explore some results about harmonic mappings from the point of view of stochastic calculus in manifolds
Mestrado
Matematica
Mestre em Matemática
APA, Harvard, Vancouver, ISO, and other styles
8

Saxcé, Nicolas de. "Sous-groupes boréliens des groupes de Lie." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112179.

Full text
Abstract:
Dans cette thèse, on étudie les sous-groupes boréliens des groupes de Lie et leur dimension de Hausdorff. Si G est un groupe de Lie nilpotent connexe, on construit dans G des sous-groupes de dimension de Hausdorff arbitraire, tandis que si G est semisimple compact, on démontre que la dimension de Hausdorff d'un sous-groupe borélien strict de G ne peut pas être arbitrairement proche de celle de G
Given a Lie group G, we investigate the possible Hausdorff dimensions for a measurable subgroup of G. If G is a connected nilpotent Lie group, we construct measurable subgroups of G having arbitrary Hausdorff dimension, whereas if G is compact semisimple, we show that a proper measurable subgroup of G cannot have Hausdorff dimension arbitrarily close to the dimension of G
APA, Harvard, Vancouver, ISO, and other styles
9

Lingenbrink, David Alan Jr. "A New Subgroup Chain for the Finite Affine Group." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/55.

Full text
Abstract:
The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.
APA, Harvard, Vancouver, ISO, and other styles
10

McDermott, Matthew. "Fast Algorithms for Analyzing Partially Ranked Data." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/58.

Full text
Abstract:
Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe how to use permutation representations of the symmetric group to create and study efficient algorithms that yield such decompositions.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Lie Groups, Harmonic and Fourier Analysis"

1

V, Volchkov Vitaly, and SpringerLink (Online service), eds. Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group. London: Springer London, 2009.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Mass.) AMS Special Session on Radon Transforms and Geometric Analysis (2012 Boston. Geometric analysis and integral geometry: AMS special session in honor of Sigurdur Helgason's 85th birthday, radon transforms and geometric analysis, January 4-7, 2012, Boston, MA ; Tufts University Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces, January 8-9, 2012, Medford, MA. Edited by Quinto, Eric Todd, 1951- editor of compilation, Gonzalez, Fulton, 1956- editor of compilation, Christensen, Jens Gerlach, 1975- editor of compilation, and Tufts University. Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces. Providence, Rhode Island: American Mathematical Society, 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Carmona, Jacques, Patrick Delorme, Michèle Vergne, and M.I.T., eds. Non-Commutative Harmonic Analysis and Lie Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0073014.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Fujiwara, Hidenori, and Jean Ludwig. Harmonic Analysis on Exponential Solvable Lie Groups. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55288-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Faraut, Jacques. Analysis on Lie groups: An introduction. Cambridge, N.Y: Cambridge University Press, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Varadarajan, V. S. An introduction to harmonic analysis on semisimple Lie groups. Cambridge, U.K: Cambridge University Press, 1999.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Varadarajan, V. S. An introduction to harmonic analysis on semisimple Lie groups. Cambridge: Cambridge University Press, 1989.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Graham, Colin C. Interpolation and Sidon Sets for Compact Groups. Boston, MA: Springer US, 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Harmonic analysis on the Heisenberg group. Boston: Birkhauser, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Lie Groups, Harmonic and Fourier Analysis"

1

Fan, Dashan. "Hp Theory on Compact Lie Groups." In Harmonic Analysis in China, 80–102. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0141-7_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Bruno, Tommaso, Marco M. Peloso, and Maria Vallarino. "Potential Spaces on Lie Groups." In Geometric Aspects of Harmonic Analysis, 149–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72058-2_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Fischer, Véronique, and Michael Ruzhansky. "A Pseudo-differential Calculus on Graded Nilpotent Lie Groups." In Fourier Analysis, 107–32. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02550-6_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Sun, Li-min. "Hermitian nilpotent lie groups: Harmonic analysis as spectral theory of Laplacians." In Harmonic Analysis, 182–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0087770.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Varadarajan, V. "Eigenfunction Expansions On Semisimple Lie Groups." In Harmonic Analysis and Group Representation, 349–422. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11117-4_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Wolf, Joseph. "Compact Lie groups and homogeneous spaces." In Harmonic Analysis on Commutative Spaces, 119–40. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/142/06.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Helgason, Sigurdur. "Representations of Semisimple Lie Groups." In Theory of Group Representations and Fourier Analysis, 65–118. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11012-2_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Sheng, Gong. "Spherical Summation of Fourier Series on Rotation Groups." In Harmonic Analysis on Classical Groups, 174–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58189-2_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Sheng, Gong. "Abel Summation of Fourier Series on Unitary Groups." In Harmonic Analysis on Classical Groups, 11–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58189-2_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Sheng, Gong. "Cesàro Summations of Fourier Series on Unitary Groups." In Harmonic Analysis on Classical Groups, 45–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58189-2_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Lie Groups, Harmonic and Fourier Analysis"

1

Bonmassar, G., and E. L. Schwartz. "Lie groups, space-variant Fourier analysis and the exponential chirp transform." In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/cvpr.1996.517117.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Yan Yan and Gregory Chirikjian. "Voronoi cells in lie groups and coset decompositions: Implications for optimization, integration, and fourier analysis." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6760035.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Antaal, Bikramjit Singh, Yogeshwar Hari, and Dennis K. Williams. "Implementation of Fourier Series in the Seismic Response Spectrum Analysis of Ground Supported Tanks." In ASME 2010 Power Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/power2010-27257.

Full text
Abstract:
This paper describes the finite element considerations employed in a seismic response spectrum analysis of a ground supported, liquid containing tank. Like many axisymmetric cylindrical vessels, the gross seismic response to an input response spectrum can be categorized by a simplified lumped mass model that includes both the mass of the tank proper in combination with the associated mass of multiple fluid levels. This simplified response may be utilized to determine the initial sizing of the supporting configuration, but lacks the ability to properly address the fluid-structure interaction that creates sloshing loads on the tank walls. The most obvious method to address the fluid-structure interaction when considering the finite element method is to build a three-dimensional model of the tank, including, but not limited to the shell courses, the top and bottom heads (for a vertical vessel), and any tank supports. The inclusion of the fluid effects may now be incorporated with “contained fluid” finite elements, however, for tanks of any significant volume, the number of finite elements can easily exceed 100,000 and the number of degrees of freedom can sore from as few as 300,000 to as many as 500,000 or more. While these types of finite element analysis problems can be solved with today’s computer hardware and software, it is not desirable in any analysis to have that volume of information that has to be subjected to the nuclear QA environment (if at all possible). With these items in mind, the methodology described in this paper seeks to minimize the number of degrees of freedom associated with a response spectrum analysis of a liquid filled, vertical cylindrical tank. The input response spectra are almost always provided in Cartesian coordinates, while many, if not most liquid containing pressure tanks are almost always axisymmetric in geometry without having benefit of being subjected to an axisymmetric load (acceleration in this case) due to the specified seismic event. The use of harmonic finite elements for both the tank structure and the contained fluid medium permit the efficiencies associated with an axisymmetric geometry to be leveraged when the seismic response spectrum is formulated in terms of a Fourier series and combined to regain the effects of the two orthogonal, horizontally applied accelerations as a function of frequency. The end result as discussed and shown in this paper is a finite element model that permits a dense mesh of both the fluid and the structure, while economizing on the number of simultaneous equations required to be solved during the chosen finite element analysis.
APA, Harvard, Vancouver, ISO, and other styles
4

Wang, Dingxi, and Sen Zhang. "An Approximate Time Domain Nonlinear Harmonic Method for Analyzing Unsteady Flows With Multiple Fundamental Modes." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-81564.

Full text
Abstract:
Abstract In this paper, a new hybrid time and frequency domain method called the approximate time domain nonlinear harmonic method is proposed for a robust and efficient analysis of turbo-machinery unsteady flow with more than one fundamental modes. The proposed method combines the features of the nonlinear harmonic method and the time domain harmonic balance method. Unsteady flow components are grouped according to their fundamental frequencies and inter blade phase angles and separate unsteady flow governing equations are constructed for each mode group. These mode groups are connected using the least squares method based Fourier transform. The proposed method is expected to be exact for a linear problem, but approximate for a nonlinear problem. Three sets of analyses with increasing level of difficulties are presented to demonstrate the validity and effectiveness of the proposed method by comparing it with the time domain harmonic balance method based upon the almost periodic Fourier transform.
APA, Harvard, Vancouver, ISO, and other styles
5

Antaal, Bikramjit Singh, Yogeshwar Hari, and Dennis K. Williams. "The Application of Harmonic Finite Elements in the Seismic Response Spectrum Analysis of a Skirt Supported Vessel." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-25886.

Full text
Abstract:
This paper describes the finite element considerations employed in a seismic response spectrum analysis of a skirt supported, liquid containing pressure vessel. Like many axisymmetric cylindrical vessels, the gross seismic response to an input response spectrum can be categorized by a simplified lump mass model that includes both the mass of the vessel proper in combination with the associated mass of multiple fluid levels. This simplified response may be utilized to determine the initial sizing of the supporting configuration, such as a skirt, but lacks the ability to properly address the fluid-structure interaction that creates sloshing loads on the vessel walls. The most obvious method to address the fluid-structure interaction when considering the finite element method is to build a three-dimensional model of the vessel proper, including, but not limited to the shell courses, the top and bottom heads (for a vertical vessel), and the support skirt. The inclusion of the fluid effects may now be incorporated with a “contained fluid” finite element, however, for vessels of any significant volume, the number of finite elements can easily exceed 100,000 and the number of degrees of freedom can sore from as few as 300,000 to as many as 500,000 or more. While these types of finite element analysis problems can be solved with today’s computer hardware and software, it is not desirable in any analysis to have that volume of information that has to be reviewed and approved in a highly regulated nuclear QA environment (if at all possible). With these items in mind, the methodology described in this paper seeks to minimize the number of degrees of freedom associated with a response spectrum analysis of a liquid filled, skirt supported vertical pressure vessel. The input response spectra are almost always provided in Cartesian coordinates, while many, if not most liquid containing pressure vessels are almost always axisymmetric in geometry without having benefit of being subjected to an axisymmetric load (acceleration in this case) due to the specified seismic event. The use of harmonic finite elements for both the vessel structure and the contained fluid medium permit the efficiencies associated with an axisymmetric geometry to be leveraged when the seismic response spectrum is formulated in terms of a Fourier series and combined to regain the effects of the two orthogonal, horizontally applied accelerations as a function of frequency. The end result as discussed and shown in this paper is a finite element model that permits a dense mesh of both the fluid and the structure, while economizing on the number of simultaneous equations required to be solved by the chosen finite element analysis.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Lie Groups, Harmonic and Fourier Analysis' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography