Harmonic analysis on symmetric spaces : Euclidean space, the sphere, and the Poincaré upper half-plane
This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal st...
Kaydedildi:
| Yazar: | |
|---|---|
| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
New York, NY :
Springer New York
2013.
Cham : Springer Nature |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Harmonic analysis on symmetric spaces, Euclidean space, the sphere, and the Poincarée upper half-plane, Audrey Terras, Second edition, New York, Springer, 2013, 1 vol. (XVII-413 p.), 1-461-47971-1 • Harmonic Analysis on Symmetric Spaces Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, Texte imprimé, 9781461479734 • Harmonic Analysis on Symmetric Spaces Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, Texte imprimé, 9781493950133 |
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| 001 | 946856 | ||
| 008 | 131018s2013 xx ||| |||| 00| 0 eng d | ||
| 009 | PPN172420350 | ||
| 020 | |a 9781461479727 | ||
| 020 | |a 9781461479727 | ||
| 041 | 0 | |a eng | |
| 082 | |a 515.785 | ||
| 100 | 1 | |a Terras, Audrey, |d 1942- | |
| 245 | 1 | 0 | |a Harmonic analysis on symmetric spaces : |b Euclidean space, the sphere, and the Poincaré upper half-plane |c by Audrey Terras. |
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c 2013. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a Chapter 1 Flat Space. Fourier Analysis on R^m. -- 1.1 Distributions or Generalized Functions -- 1.2 Fourier Integrals -- 1.3 Fourier Series and the Poisson Summation Formula -- 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions -- 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyl s Criterion for Uniform Distribution -- Chapter 2 A Compact Symmetric Space--The Sphere -- 2.1 Fourier Analysis on the Sphere -- 2.2 O(3) and R^3. The Radon Transform -- Chapter 3 The Poincaré Upper Half-Plane -- 3.1 Hyperbolic Geometry -- 3.2 Harmonic Analysis on H -- 3.3 Fundamental Domains for Discrete Subgroups of G = SL(2, R) -- 3.4 Modular of Automorphic Forms--Classical -- 3.5 Automorphic Forms--Not So Classical--Maass Waveforms -- 3.6 Modular Forms and Dirichlet Series. Hecke Theory and Generalizations -- References -- Index. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections, new topics, and updates have been incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maass waveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg trace formula and its applications in spectral theory as well as number theory. | ||
| 776 | 0 | |0 18098618X |t Harmonic analysis on symmetric spaces |o Euclidean space, the sphere, and the Poincarée upper half-plane |f Audrey Terras |e Second edition |c New York |n Springer |d 2013 |p 1 vol. (XVII-413 p.) |z 1-461-47971-1 | |
| 776 | 0 | |t Harmonic Analysis on Symmetric Spaces Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane |b Texte imprimé |z 9781461479734 | |
| 776 | 0 | |t Harmonic Analysis on Symmetric Spaces Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane |b Texte imprimé |z 9781493950133 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-1-4614-7972-7 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-41PFWKN9-L |z Accès sur la plateforme Istex | |
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