Relevant bibliographies by topics / Dualité de Pontryagin

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  2. Dissertations / Theses
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Academic literature on the topic 'Dualité de Pontryagin'

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Published: 14 December 2024

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Journal articles on the topic "Dualité de Pontryagin"

1

Lim, Johnny. "Analytic Pontryagin duality." Journal of Geometry and Physics 145 (November 2019): 103483. http://dx.doi.org/10.1016/j.geomphys.2019.103483.

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Chasco, M. J., and E. Mart�n-Peinador. "Binz-Butzmann duality versus Pontryagin duality." Archiv der Mathematik 63, no. 3 (September 1994): 264–70. http://dx.doi.org/10.1007/bf01189829.

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Banaszczyk, Wojciech, María Jesús Chasco, and Elena Martin-Peinador. "Open subgroups and Pontryagin duality." Mathematische Zeitschrift 215, no. 1 (January 1994): 195–204. http://dx.doi.org/10.1007/bf02571709.

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Chasco, M. J. "Pontryagin duality for metrizable groups." Archiv der Mathematik 70, no. 1 (January 1, 1998): 22–28. http://dx.doi.org/10.1007/s000130050160.

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Shtern, A. I. "Duality between compactness and discreteness beyond pontryagin duality." Proceedings of the Steklov Institute of Mathematics 271, no. 1 (December 2010): 212–27. http://dx.doi.org/10.1134/s0081543810040164.

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Melnikov, Alexander. "Computable topological groups and Pontryagin duality." Transactions of the American Mathematical Society 370, no. 12 (May 3, 2018): 8709–37. http://dx.doi.org/10.1090/tran/7355.

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Hern�ndez, Salvador. "Pontryagin duality for topological Abelian groups." Mathematische Zeitschrift 238, no. 3 (November 1, 2001): 493–503. http://dx.doi.org/10.1007/s002090100263.

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Van Daele, A., and Shuanhong Wang. "Pontryagin duality for bornological quantum hypergroups." manuscripta mathematica 131, no. 1-2 (November 18, 2009): 247–63. http://dx.doi.org/10.1007/s00229-009-0318-8.

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Hernández, Salvador, and Vladimir Uspenskij. "Pontryagin Duality for Spaces of Continuous Functions." Journal of Mathematical Analysis and Applications 242, no. 2 (February 2000): 135–44. http://dx.doi.org/10.1006/jmaa.1999.6627.

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Gabriyelyan, S. S. "Groups of quasi-invariance and the Pontryagin duality." Topology and its Applications 157, no. 18 (December 2010): 2786–802. http://dx.doi.org/10.1016/j.topol.2010.08.018.

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Dissertations / Theses on the topic "Dualité de Pontryagin"

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Artusa, Marco. "Sur des théorèmes de dualité pour la cohomologie condensée du groupe de Weil d'un corps p-adique." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0228.

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L’objectif de cette thèse est double. Premièrement, on construit une théorie de cohomologie topologique pour le groupe de Weil d’un corps p-adique. En second lieu, on utilise cette théorie pour prouver des théorèmes de dualité, qui se manifestent sous la forme de la dualité de Pontryagin entre groupes abéliens localement compacts. Ces résultats améliorent des théorèmes de dualité existants et leur confèrent une perspective topologique. De tels objectifs peuvent être atteints grâce aux Mathématiques Condensées, qui fournissent un cadre dans lequel il est possible de faire de l’algèbre avec des objets topologiques. On définit une théorie cohomologique pour les groupes condensés et pro-condensés et on étudie ses propriétés. Ensuite, on applique cela au groupe de Weil d’un corps p-adique, considéré comme un groupe pro-condensé. On démontre que, dans certains cas particuliers, les groupes de cohomologie correspondants sont des groupes abéliens localement compacts de rangs finis. Ceci nous permet d’étendre la dualité locale de Tate à une catégorie plus générale de coefficients non nécessairement discrets, o`u elle prend la forme d’une dualité de Pontryagin entre groupes abéliens localement compacts. Dans la dernière partie de la thèse, on utilise le même cadre pour retrouver une version “à la Weil” de la dualité de Tate avec coefficients dans les variétés abéliennes, et plus généralement dans les 1- motifs, en exprimant ces dualités comme des accouplements parfaits entre groupes abéliens condensés. Pour ce faire, on associe à chaque groupe algébrique, resp. 1-motif, un groupe abélien condensé, resp. un complexe de groupes abéliens condensés, avec une action du groupe de Weil (pro-condensé). On appelle cette association la réalisation de Weil-étale condensée. On montre l’existence d’un accouplement de Poincaré condensé pour les variétés abéliennes, et on prouve une version condensée et “à la Weil” de la dualité de Tate à coefficients dans les variétés abéliennes, qui améliore le résultat correspondant de Karpuk. Enfin, on montre l’existence d’un accouplement de Poincaré condensé pour les 1-motifs. On prouve que cet accouplement est compatible à la filtration par les poids et on démontre un théorème de dualité à coefficients dans les 1- motifs, qui améliore un résultat de Harari-Szamuely
The goal of this thesis is twofold. First, we build a topological cohomology theory for the Weil group of p-adic fields. Secondly, we use this theory to prove duality theorems for such fields, which manifest as Pontryagin duality between locally compact abelian groups. These results improve existing duality theorems and give them a topological flavour. Condensed Mathematics allow us to reach these objectives, providing a framework where it is possible to do algebra with topological objects. We define and study a cohomology theory for condensed groups and pro-condensed groups, and we apply it to the Weil group of a p-adic field, considered as a pro-condensed group. The resulting cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups. In the last part of the thesis, we use the same framework to recover a Weil-version of the Tate duality with coefficients in abelian varieties and more generally in 1-motives, expressing those dualities as perfect pairings between condensed abelian groups. To do this, we associate to every algebraic group, resp. 1-motive, a condensed abelian group, resp. a complex of condensed abelian groups, with an action of the (pro-condensed) Weil group. We call this association the condensed Weil-´etale realisation. We show the existence of a condensed Poincar´e pairing for abelian varieties and we prove a condensed-Weil version of the Tate duality with coefficients in abelian varieties, which improves the correspondent result of Karpuk. Lastly, we exhibit a condensed Poincar´e pairing for 1-motives. We show that this pairing is compatible with the weight filtration and we prove a duality theorem with coefficients in 1-motives, which improves a result of Harari-Szamuely
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Del, Gatto Davide. "Analisi di Fourier sui Gruppi." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18784/.

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La tesi riguarda la generalizzazione della trasformata di Fourier per funzioni di L^1(G), dove G è un gruppo topologico localmente compatto e di Hausdroff. L'obbiettivo è di mostrare che i risultati noti per la trasformata di Fourier (come il Teorema di Inversione, il Teorema di Plancherel, ecc...) sono validi anche in questo caso e di presentare alcuni risultati classici di analisi armonica astratta nel caso di gruppi abeliani come il Teorema di Dualità di Pontryagin.
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Chis, Cristina. "Bounded sets in topological groups." Doctoral thesis, Universitat Jaume I, 2010. http://hdl.handle.net/10803/10502.

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A boundedness structure (bornology) on a topological space is an ideal of subsets containing all singletons, that is, closed under taking subsets and unions of finitely many elements. In this paper we deal with the structure of the whole family of bounded subsets rather than the specific properties of them by means of certain functions that we define on a metrizable topological group. Our motivation is twofold: on the one hand, we obtain useful information about the structural features of certain remarkable classes of bounded systems, cofinality, local properties, etc. For example, we estimate the cofinality of these boundedness notions.
In the second part of the paper, we apply duality methods in order to obtain estimations of the size of a local base for an important class of groups. This translation, which has been widely exhibited in the Pontryagin-van Kampen duality theory of locally compact abelian groups, is often very relevant and has been extended by many authors to more general classes of topological groups. In this work we follow basically the pattern and terminology given by Vilenkin in 1998.
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Lim, Johnny. "Analytic Pontryagin Duality." Thesis, 2019. http://hdl.handle.net/2440/124554.

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Let X be a smooth compact manifold. We propose a geometric model for the group K⁰(X,R/Z): We study a well-defined and non-degenerate analytic duality pairing between K⁰(X,R/Z) and its Pontryagin dual group, the Baum-Douglas geometric K-homology K₀(X); whose pairing formula comprises of an analytic term involving the Dai-Zhang eta-invariant associated to a twisted Dirac-type operator and a topological term involving a differential form and some characteristic forms. This yields a robust R/Z-valued invariant. We also study two special cases of the analytic pairing of this form in the cohomology groups H¹(X,R/Z) and H²(X,R/Z):
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2019
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Černohorská, Eva. "Homotopické struktury v algebře, geometrii a matematické fyzice." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313715.

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Title: Homotopic structures in algebra, geometry and mathematical physics Author: Eva Černohorská Department: Mathematical Institute of Charles University Supervisor: RNDr. Martin Markl, DrSc., Institute of Mathematics of the Academy of Sciences of the Czech Republic, Mathematical Institute of Charles University Abstract: The aim of this thesis was to generalize the result that associative algebras on finite dimensional vector spaces can be described using differentials on free algebras. This result is limited by the duality of vector spaces. If we assume that the underlying space has a linear topology, then we can use the duality between discrete and linearly compact (profinite) vector spaces. To generalize the notion of an algebra, we need to recall the completed tensor product on linear vector spaces. Since this topics does not seem to be sufficiently covered by the literature, this thesis could serve also as a comprehensive text on linear vector spaces and their completed tensor products. We prove that also A∞ structures on linearly compact vector spaces could be represented by differentials on a free algebra. Keywords: Strongly homotopy associative algebra, linear topological vector space, Pontryagin duality, completed tensor product, differential
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Books on the topic "Dualité de Pontryagin"

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Außenhofer, Lydia, Dikran Dikranjan, and Anna Giordano Bruno. Topological Groups and the Pontryagin-van Kampen Duality. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110654936.

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Dikranjan, Dikran, Anna Giordano Bruno, and Lydia Außenhofer. Topological Groups and the Pontryagin-Van Kampen Duality: An Introduction. de Gruyter GmbH, Walter, 2021.

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Stralka, A., M. Mislove, and K. H. Hofmann. Pontryagin Duality of Compact o-Dimensional Semilattices and Its Applications. Springer London, Limited, 2006.

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Dikranjan, Dikran, Anna Giordano Bruno, and Lydia Außenhofer. Topological Groups and the Pontryagin-Van Kampen Duality: An Introduction. de Gruyter GmbH, Walter, 2021.

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Dikranjan, Dikran, Anna Giordano Bruno, and Lydia Außenhofer. Topological Groups and the Pontryagin-Van Kampen Duality: An Introduction. de Gruyter GmbH, Walter, 2021.

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Morris, Sidney A. Pontryagin Duality and the Structure of Locally Compact Abelian Groups. Cambridge University Press, 2009.

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Morris, Sidney A. Pontryagin Duality and the Structure of Locally Compact Abelian Groups. Cambridge University Press, 2011.

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Zhang, Xu, and Qi Lü. General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions. Springer London, Limited, 2014.

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General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions. Springer, 2014.

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Book chapters on the topic "Dualité de Pontryagin"

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Banaszczyk, Wojciech. "Pontryagin duality." In Lecture Notes in Mathematics, 132–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0089152.

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Vourdas, Apostolos. "Partial Orders and Pontryagin Duality." In Quantum Science and Technology, 7–10. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59495-8_2.

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Jayakumar, S., S. S. Iyengar, and Naveen Kumar Chaudhary. "Sensor Fusion and Pontryagin Duality." In Lecture Notes in Electrical Engineering, 123–37. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-5091-1_10.

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Lisica, Yu T. "The alexander-pontryagin duality theorem for coherent homology and cohomology with coefficients in sheaves of modules." In Lecture Notes in Mathematics, 148–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0081425.

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Gamkrelidze, R. V. "Topological Duality Theorems." In L. S. Pontryagin Selected Works, 347–74. CRC Press, 2019. http://dx.doi.org/10.1201/9780367813758-25.

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"13 The Pontryagin-van Kampen duality." In Topological Groups and the Pontryagin-van Kampen Duality, 201–28. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110654936-013.

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Gamkrelidze, R. V. "The General Topological Theorem of Duality for Closed Sets *." In L. S. Pontryagin Selected Works, 137–50. CRC Press, 2019. http://dx.doi.org/10.1201/9780367813758-9.

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"14 Applications of the duality theorem." In Topological Groups and the Pontryagin-van Kampen Duality, 229–62. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110654936-014.

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"7 Completeness and completion." In Topological Groups and the Pontryagin-van Kampen Duality, 97–114. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110654936-007.

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"11 The Følner theorem." In Topological Groups and the Pontryagin-van Kampen Duality, 159–86. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110654936-011.

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Conference papers on the topic "Dualité de Pontryagin"

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Akbarov, Sergei S. "Pontryagin duality and topological algebras." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-5.

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Gauthier, Jean Paul. "Hypoelliptic diffusion, Chu duality and human vision." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Moscow: Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22841.

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You might also be interested in the extended bibliographies on the topic 'Dualité de Pontryagin' for particular source types:
Journal articles
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