000			04317nam a22005535i 4500
001			978-1-4614-7972-7
003			DE-He213
005			20180115171530.0
007			cr nn 008mamaa
008			130912s2013 xxu| s |||| 0|eng d
020			_a9781461479727 _9978-1-4614-7972-7
024	7		_a10.1007/978-1-4614-7972-7 _2doi
050		4	_aQA403-403.3
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.785 _223
100	1		_aTerras, Audrey. _eauthor.
245	1	0	_aHarmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane _h[electronic resource] / _cby Audrey Terras.
250			_a2nd ed. 2013.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXVII, 413 p. 83 illus., 32 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_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 Γ 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.
520			_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 Γ, 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.
650		0	_aMathematics.
650		0	_aGroup theory.
650		0	_aTopological groups.
650		0	_aLie groups.
650		0	_aHarmonic analysis.
650		0	_aFourier analysis.
650		0	_aFunctions of complex variables.
650		0	_aSpecial functions.
650	1	4	_aMathematics.
650	2	4	_aAbstract Harmonic Analysis.
650	2	4	_aFourier Analysis.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aSpecial Functions.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461479710
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-7972-7
912			_aZDB-2-SMA
999			_c370781 _d370781