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A gaussian space of test functions

✍ Scribed by J. Jorgenson; S. Lang

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
146 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Elsewhere we develop an aspect of analysis on the simplest space of type G/K when G = SL~2~(C) and K is the unitary subgroup, having to do with the analogue of Poisson's inversion formula and resulting additive zeta functions obtained by applying the Gauss transform. The present paper carries out systematically a number of foundational properties of gaussians on that space, which serve as test functions, give rise to explicit formulas, and lead immediately into the heat kernel, which is a gaussian. We prove approximation properties and the fact that the space of gaussians is dense in essentially anything space one wants. (Β© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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