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Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis
Author(s) -
Constales D.,
S. Kraußhar R.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.385
Subject(s) - mathematics , dimension (graph theory) , pure mathematics , mathematical analysis , integrable system , euclidean space , trigonometric functions , square integrable function , domain (mathematical analysis) , bergman space , kernel (algebra) , space (punctuation) , function (biology) , geometry , linguistics , philosophy , evolutionary biology , biology , bounded function
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.