Analytic continuation and identities involving heat, Poisson, wave and Bessel kernels
✍ Scribed by Jay Jorgenson; Serge Lang
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 313 KB
- Volume
- 258
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
In this article we use classical formulas involving the K–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromorphic continuation of the associated Poisson kernel to all values of complex time with identifiable singularities. This result reproves in a different setting by different means a well–known theorem due to Duistermaat and Guillemin [DG 75]. Also, we develop analytic expressions for the heat kernel beyond asymptotic expansions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)