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

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ISBN: 978-1-84882-532-1 (Print) 978-1-84882-533-8 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages i-xi

  2. Symmetric Spaces. Harmonic Analysis on Spheres

    1. Front Matter

      Pages 1-3

    2. No Access

      Book Chapter

      Pages 5-33

      General Considerations

    3. No Access

      Book Chapter

      Pages 35-60

      Analogues of the Beltrami–Klein Model for Rank One Symmetric Spaces of Noncompact Type

    4. No Access

      Book Chapter

      Pages 61-83

      Realizations of Rank One Symmetric Spaces of Compact Type

    5. No Access

      Book Chapter

      Pages 85-134

      Realizations of the Irreducible Components of the Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces

    6. No Access

      Book Chapter

      Pages 135-152

      Non-Euclidean Analogues of Plane Waves

    7. Back Matter

      Pages 153-156

  3. Transformations with Generalized Transmutation Property Associated with Eigenfunctions Expansions

    1. Front Matter

      Pages 157-159

    2. No Access

      Book Chapter

      Pages 161-176

      Preliminaries

    3. No Access

      Book Chapter

      Pages 177-200

      Some Special Functions

    4. No Access

      Book Chapter

      Pages 201-229

      Exponential Expansions

    5. No Access

      Book Chapter

      Pages 231-267

      Multidimensional Euclidean Case

    6. No Access

      Book Chapter

      Pages 269-334

      The Case of Symmetric Spaces X=G/K of Noncompact Type

    7. No Access

      Book Chapter

      Pages 335-370

      The Case of Compact Symmetric Spaces

    8. No Access

      Book Chapter

      Pages 371-394

      The Case of Phase Space

    9. Back Matter

      Pages 395-399

  4. Mean Periodicity

    1. Front Matter

      Pages 401-403

    2. No Access

      Book Chapter

      Pages 405-440

      Mean Periodic Functions on Subsets of the Real Line

    3. No Access

      Book Chapter

      Pages 441-486

      Mean Periodic Functions on Multidimensional Domains

    4. No Access

      Book Chapter

      Pages 487-522

      Mean Periodic Functions on G/K

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      Book Chapter

      Pages 523-544

      Mean Periodic Functions on Compact Symmetric Spaces of Rank One

    6. No Access

      Book Chapter

      Pages 545-557

      Mean Periodicity on Phase Space and the Heisenberg Group

    7. Back Matter

      Pages 559-569

  5. Local Aspects of Spectral Analysis and the Exponential Representation Problem

    1. Front Matter

      Pages 571-574

    2. No Access

      Book Chapter

      Pages 575-596

      A New Look at the Schwartz Theory

    3. No Access

      Book Chapter

      Pages 597-614

      Recent Developments in the Spectral Analysis Problem for Higher Dimensions

    4. No Access

      Book Chapter

      Pages 615-631

      ℰ′ (X) Spectral Analysis on Domains of Noncompact Symmetric Spaces of Arbitrary Rank

    5. Back Matter

      Pages 639-646

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