The Resource Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, by Audrey Terras, (electronic resource)

Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, by Audrey Terras, (electronic resource)

Label
Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane
Title
Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane
Statement of responsibility
by Audrey Terras
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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 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
http://library.link/vocab/creatorName
Terras, Audrey
Image bit depth
0
LC call number
QA403-403.3
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
http://library.link/vocab/subjectName
  • Mathematics
  • Group theory
  • Topological Groups
  • Harmonic analysis
  • Fourier analysis
  • Functions of complex variables
  • Functions, special
  • Mathematics
  • Abstract Harmonic Analysis
  • Fourier Analysis
  • Group Theory and Generalizations
  • Topological Groups, Lie Groups
  • Functions of a Complex Variable
  • Special Functions
Label
Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, by Audrey Terras, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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 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
Dimensions
unknown
Edition
2nd ed. 2013.
Extent
XVII, 413 p. 83 illus., 32 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9781461479727
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-1-4614-7972-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-1-4614-7972-7
Label
Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane, by Audrey Terras, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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 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
Dimensions
unknown
Edition
2nd ed. 2013.
Extent
XVII, 413 p. 83 illus., 32 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9781461479727
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-1-4614-7972-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-1-4614-7972-7

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...