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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weighted Laplace transforms and
Bessel functions on Hermitian symmetric spaces


Author: Hongming Ding
Journal: Trans. Amer. Math. Soc. 351 (1999), 4205-4243
MSC (1991): Primary 22E46, 43A85, 17C30, 33C10; Secondary 22E30, 17C50, 33B15
Published electronically: June 10, 1999
MathSciNet review: 1653347
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Abstract: This paper defines $\pi $-weighted Laplace transforms on the spaces of $\pi $-covariant functions. By the inverse Laplace transform we define operator-valued Bessel functions. We also study the holomorphic discrete series of the automorphism group of a Siegel domain of type II.


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Additional Information

Hongming Ding
Affiliation: Department of Mathematics and Computer Science, St. Louis University, St. Louis, Missouri 63103
Email: dingh@sluvca.slu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02461-7
PII: S 0002-9947(99)02461-7
Keywords: $\pi $-weighted Laplace transform, Jordan pair, Siegel domain of type II, Bessel function, holomorphic discrete series
Received by editor(s): March 22, 1994
Received by editor(s) in revised form: January 9, 1997
Published electronically: June 10, 1999
Additional Notes: This research was supported in part by the National Science Foundation grant DMS-9312465.
Article copyright: © Copyright 1999 American Mathematical Society