Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis
D Constales, R S. Kraußhar - Mathematical Methods in the …, 2002 - Wiley Online Library
D Constales, R S. Kraußhar
Mathematical Methods in the Applied Sciences, 2002•Wiley Online LibraryIn 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 …
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 …
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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