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Weighted Laplace transforms and Bessel functions on Hermitian symmetric spaces

Author(s): Hongming Ding
Journal: Trans. Amer. Math. Soc. 351 (1999), 4205-4243.
MSC (1991): Primary 22E46, 43A85, 17C30, 33C10; Secondary 22E30, 17C50, 33B15
Posted: June 10, 1999
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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: 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
Posted: June 10, 1999
Additional Notes: This research was supported in part by the National Science Foundation grant DMS-9312465.
Copyright of article: Copyright 1999, American Mathematical Society

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