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15 The Whittaker Plancherel Theorem

Publisher
Elsevier B.V.
Identifiers
DOI: 10.1016/s0079-8169(08)62840-8
Disciplines
  • Mathematics

Abstract

Publisher Summary This chapter discusses the derivation of decomposition into the irreducibles of an important class of induced representations. It describes the way this technique can be used to derive asymptotic expansions for certain generalized matrix coefficients of admissible representations. It contains a rapid development of the theory of cusp forms for the case at hand. The Jucquet integrals are introduced in the chapter that play the role of matrix coefficients and Eisenstein integrals. Armed with the continuation of the Jacquet integral, a complete description of the discrete spectrum for the case of generic x can be given. The development of the material presented in the chapter uses the Harish-Chandra Plancherel theorem. The chapter discusses several special cases of the theorem and shows the way the Lebedev inversion formula can be derived from the result for SL(2,R).

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