Bounds for Fourier transforms of regular orbital integrals on adic Lie algebras
Author:
Rebecca A. Herb
Journal:
Represent. Theory 5 (2001), 504523
MSC (2000):
Primary 22E30, 22E45
Published electronically:
November 16, 2001
MathSciNet review:
1870601
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Abstract: Let be a connected reductive adic group and let be its Lie algebra. Let be a orbit in . Then the orbital integral corresponding to is an invariant distribution on , and HarishChandra proved that its Fourier transform is a locally constant function on the set of regular semisimple elements of . Furthermore, he showed that a normalized version of the Fourier transform is locally bounded on . Suppose that is a regular semisimple orbit. Let be any semisimple element of , and let be the centralizer of . We give a formula for (in terms of Fourier transforms of orbital integrals on ), for regular semisimple elements in a small neighborhood of in and sufficiently large. We use this result to prove that HarishChandra's normalized Fourier transform is globally bounded on in the case that is a regular semisimple orbit.
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Additional Information
Rebecca A. Herb
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland, 20742
Email:
rah@math.umd.edu
DOI:
http://dx.doi.org/10.1090/S108841650100125X
PII:
S 10884165(01)00125X
Received by editor(s):
March 14, 2001
Published electronically:
November 16, 2001
Additional Notes:
Supported in part by NSF Grant DMS 0070649
Article copyright:
© Copyright 2001
American Mathematical Society
