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Square Integrable Representations, Spherical Functions and Trace Formulas

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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL,volume 198)

Abstract

This chapter deals with one of the central topics of this book. The first section contains important basic facts from the theory of representations of compact groups and it should be read in full even if some of the later sections are omitted. Section 2 is essential for the formulation and proof of the Selberg—Tamagawa trace formula which is given in Section 6. Its proof is independent of the material discussed in Sections 3, 4 and 5. However the last section contains the statement and proof of a class of trace formulas which can be appreciated only by knowing about spherical functions as defined by Godement and Harish—Chandra. The theory of these is developed in Section 3. Moreover it is necessary to know from Section 4 and 5 at least the statements of Theorems 4.1 and 5.10.

Keywords

  • Irreducible Representation
  • Irreducible Component
  • Compact Group
  • Unitary Representation
  • Compact Subgroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1973 Springer-Verlag Berlin Heidelberg

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Gaal, S.A. (1973). Square Integrable Representations, Spherical Functions and Trace Formulas. In: Linear Analysis and Representation Theory. Die Grundlehren der mathematischen Wissenschaften, vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80741-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-80741-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-80743-5

  • Online ISBN: 978-3-642-80741-1

  • eBook Packages: Springer Book Archive