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- W2016061330 abstract "Let G be a connected semisimple Lie group. If G has finite center, Harish-Chandra used Eisenstein integrals to construct Schwartz class wave packets of matrix coefficients and showed that every K-finite function in the Schwartz space is a finite sum of such wave packets. This paper is the second in a series which generalizes these results of Harish-Chandra to include the case that G has infinite center. In this paper, the Plancherel theorem is used to decompose K-compact Schwartz class functions (those with K-types in a compact set) as finite sums of wave packets. A new feature of the infinite center case is that the individual wave packets occurring in the decomposition of a Schwartz class function need not be Schwartz class. These wave packets are studied to obtain necessary conditions for a wave packet of Eisenstein integrals to occur in the decomposition of a Schwartz class function. Applied to the case that a itself is a single wave packet, the results of this paper yield a complete characterization of Schwartz class wave packets." @default.
- W2016061330 created "2016-06-24" @default.
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- W2016061330 date "1991-01-01" @default.
- W2016061330 modified "2023-10-18" @default.
- W2016061330 title "The Schwartz space of a general semisimple Lie group. II. Wave packets associated to Schwartz functions" @default.
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- W2016061330 doi "https://doi.org/10.1090/s0002-9947-1991-1014250-6" @default.
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