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Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis

✍ Scribed by D. Constales; R. S. Kraußhar

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 154 KB
Volume: 25
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.385

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✦ Synopsis

Abstract

In this paper, we consider rectangular domains in real Euclidean spaces of dimension at least 2, where the sides can be finite, semi‐infinite, or fully infinite. The Bergman reproducing kernel for the space of monogenic and square integrable functions on such a domain is obtained in closed form as a finite sum of monogenic multiperiodic functions. The reproducing property leads to an estimate of the first derivative of the single‐periodic cotangent function in terms of the classical real‐valued Eisenstein series. Copyright © 2002 John Wiley Sons, Ltd.

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