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Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

This book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to harmonic analysis, complex ana...

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Bibliographic Details
Main Authors: Volchkov, Valery V., Volchkov, Vitaly V. (Author)
Format: eBook
Language:English
Published: London Springer London 2009, 2009
Edition:1st ed. 2009
Series:Springer Monographs in Mathematics
Subjects:
Functional Analysis
Integral Equations
Special Functions
Mathematical Analysis
Fourier Analysis
Approximations And Expansions
Analysis
Approximation Theory
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Symmetric Spaces. Harmonic Analysis on Spheres
  • General Considerations
  • Analogues of the Beltrami–Klein Model for Rank One Symmetric Spaces of Noncompact Type
  • Realizations of Rank One Symmetric Spaces of Compact Type
  • Realizations of the Irreducible Components of the Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces
  • Non-Euclidean Analogues of Plane Waves
  • Transformations with Generalized Transmutation Property Associated with Eigenfunctions Expansions
  • Preliminaries
  • Some Special Functions
  • Exponential Expansions
  • Multidimensional Euclidean Case
  • The Case of Symmetric Spaces X=G/K of Noncompact Type
  • The Case of Compact Symmetric Spaces
  • The Case of Phase Space
  • Mean Periodicity
  • Mean Periodic Functions on Subsets of the Real Line
  • Mean Periodic Functions on Multidimensional Domains
  • Mean Periodic Functions on G/K
  • Mean Periodic Functions on Compact Symmetric Spaces of Rank One
  • Mean Periodicity on Phase Space and the Heisenberg Group
  • Local Aspects of Spectral Analysis and the Exponential Representation Problem
  • A New Look at the Schwartz Theory
  • Recent Developments in the Spectral Analysis Problem for Higher Dimensions
  • ????(X) Spectral Analysis on Domains of Noncompact Symmetric Spaces of Arbitrary Rank
  • Spherical Spectral Analysis on Subsets of Compact Symmetric Spaces

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