LEADER 05654nam 22008535 450 001 9910438034603321 005 20200701142636.0 010 $a1-4614-7972-X 024 7 $a10.1007/978-1-4614-7972-7 035 $a(CKB)3710000000019036 035 $a(EBL)1466262 035 $a(SSID)ssj0001010503 035 $a(PQKBManifestationID)11550811 035 $a(PQKBTitleCode)TC0001010503 035 $a(PQKBWorkID)10999467 035 $a(PQKB)10814282 035 $a(DE-He213)978-1-4614-7972-7 035 $a(MiAaPQ)EBC6312947 035 $a(MiAaPQ)EBC1466262 035 $a(Au-PeEL)EBL1466262 035 $a(CaPaEBR)ebr10968918 035 $a(OCoLC)858975843 035 $a(PPN)172420350 035 $a(EXLCZ)993710000000019036 100 $a20130912d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHarmonic Analysis on Symmetric Spaces?Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane /$fby Audrey Terras 205 $a2nd ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (430 p.) 300 $aDescription based upon print version of record. 311 $a1-4614-7971-1 320 $aIncludes bibliographical references and index. 327 $aChapter 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. 330 $aThis 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. 606 $aHarmonic analysis 606 $aFourier analysis 606 $aGroup theory 606 $aTopological groups 606 $aLie groups 606 $aFunctions of complex variables 606 $aFunctions, Special 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 615 0$aHarmonic analysis. 615 0$aFourier analysis. 615 0$aGroup theory. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aFunctions of complex variables. 615 0$aFunctions, Special. 615 14$aAbstract Harmonic Analysis. 615 24$aFourier Analysis. 615 24$aGroup Theory and Generalizations. 615 24$aTopological Groups, Lie Groups. 615 24$aFunctions of a Complex Variable. 615 24$aSpecial Functions. 676 $a515.2433 700 $aTerras$b Audrey$4aut$4http://id.loc.gov/vocabulary/relators/aut$056408 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438034603321 996 $aHarmonic Analysis on Symmetric Spaces?Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane$92494433 997 $aUNINA