Дисертації з теми "Lie Groups, Harmonic and Fourier Analysis"
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Li, Jialun. "Harmonic analysis of stationary measures." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0311/document.
Повний текст джерелаLet 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
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.
Повний текст джерелаWang, Simeng. "Some problems in harmonic analysis on quantum groups." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2062/document.
Повний текст джерелаThis 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
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.
Повний текст джерелаWang, Xumin. "Functional and harmonic analysis of noncommutative Lp spaces associated to compact quantum groups." Thesis, Bourgogne Franche-Comté, 2019. http://www.theses.fr/2019UBFCD040.
Повний текст джерелаThis 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
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.
Повний текст джерелаSilva, Fabiano Borges da. "Aplicações harmonicas e martingales em variedades." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306288.
Повний текст джерелаDissertação (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
Saxcé, Nicolas de. "Sous-groupes boréliens des groupes de Lie." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112179.
Повний текст джерелаGiven 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
Lingenbrink, David Alan Jr. "A New Subgroup Chain for the Finite Affine Group." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/55.
Повний текст джерелаMcDermott, Matthew. "Fast Algorithms for Analyzing Partially Ranked Data." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/58.
Повний текст джерелаChung, Kin Hoong. "Compact group actions and harmonic analysis /." 1999. http://www.library.unsw.edu.au/~thesis/adt-NUN/public/adt-NUN20010510.153038/index.html.
Повний текст джерелаSEGUIN, CAROLINE. "Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups." Thesis, 2011. http://hdl.handle.net/1974/6834.
Повний текст джерелаThesis (Master, Mathematics & Statistics) -- Queen's University, 2011-10-08 01:32:32.896
Gallo, Andrea Lilén. "Análisis armónico en nilvariedades." Doctoral thesis, 2020. http://hdl.handle.net/11086/15949.
Повний текст джерелаEsta tesis se encuadra en el estudio del análisis armónico en pares de Gelfand de la forma (K,N), donde N es un grupo de Lie nilpotente y K es un subgrupo de automorfismos de N. En una primera parte trabajamos con una familia de pares de Gelfand (K,N) definida previamente por Jorge Lauret. Descomponemos la acción del producto semidirecto de K y N, sobre el espacio de funciones definidas sobre N de cuadrado integrable. Para estas familias, encontramos además la medida de Plancherel y la proyección sobre cada componente mediante las funciones esféricas asociadas al par. En el caso del grupo de Heisenberg se obtienen estos resultados para los pares de Gelfand asociados a cualquier K subgrupo de automorfismos del grupo de Heisenberg. Finalmente, nos avocamos al estudio de pares de Gelfand generalizados, es decir, a pares de Gelfand donde el subgrupo K no es necesariamente compacto. Un resultado clásico garantiza que si (K,N) es un par de Gelfand donde N es un grupo de Lie nilpotente y K subgrupo compacto de automorfismos de N, entonces N es a lo sumo 2-pasos nilpotente. En esta tesis, damos un ejemplo concreto de un par de Gelfand generalizado (K,N) donde N es un grupo de Lie 3-pasos nilpotente.
This thesis is part of the study of harmonic analysis in Gelfand pairs (K,N), where N is a nilpotent Lie group and K a subgroup of automorphisms of N. In the first part, we work with a family of Gelfand pairs (K,N) defined by Jorge Lauret. We decompose the action of the semidirect product of K and N in the space of square integrable functions defined on N. We also find the Plancherel measure and the projection over each component by using spherical functions associated to the pair. In the Heisenberg case we obtain similar results with every Gelfand pair associated with each automorphism subgroup of the Heisenberg group. Finally, we deal with the study of generalized Gelfand pairs, i.e when K is non-compact. A classic result assures that, if (K,N) is a Gelfand pair with N nilpotent and K compact then N is necessarily 2-step nilpotent. In this thesis, we give an explicit example of a generalized Gelfand pair (K,N) where N is a 3-step nilpotent Lie group.
Fil: Gallo, Andrea Lilén. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Williams, Michael Bradford. "Analysis of geometric flows, with applications to optimal homogeneous geometries." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-05-2820.
Повний текст джерелаtext
Avetisyan, Zhirayr. "Mode decomposition and Fourier analysis of physical fields in homogeneous cosmology." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A11872.
Повний текст джерелаLemmer, Ryan Lee. "The paradigms of mechanics : a symmetry based approach." Thesis, 1996. http://hdl.handle.net/10413/4899.
Повний текст джерелаThesis (M.Sc.)-University of Natal, 1996.
Bettadapura, Raghu Prasad Radhakrishna. "Flexible fitting in 3D EM." 2012. http://hdl.handle.net/2152/19478.
Повний текст джерелаtext
Rocha, Pablo Alejandro. "Propiedades Lp-Improving de algunos operadores de convolución con medidas singulares en Rn y en Hn /." Doctoral thesis, 2009. http://hdl.handle.net/11086/131.
Повний текст джерелаEn este trabajo estudiamos algunos operadores de convolución con medidas singulares tanto en el contexto euclídeo como en el grupo de Heisenberg Hn. Mediante técnicas de interpolación compleja y el análisis de la transformada de Fourier (la euclídea o bien la inherente al grupo de Heisenberg según el caso) de estas medidas, obtenemos propiedades Lp-improving para tales operadores. En algunos casos se caracteriza exactamente el conjunto tipo correspondiente. Esto es logrado via la obtención de estimaciones sharp para ciertas integrales oscilantes asociadas a las transformadas de Fourier mencionadas. Como subproducto de estas estimaciones se obtiene además, en el caso euclídeo estudiado, un teorema de restricción Lp ¡ L2 para la transformada de Fourier.
Pablo Alejandro Rocha.