Title: Generalizations of the Complex Analytic Trigonometric Functions to Clifford Analysis by Eisenstein Series
Authors: Krausshar, Rolf Sören
Issue Date: 2001
Publisher: World Scientific
Host Document: Functional-Analytic and complex methods, their interactions, and Applications to Partial Differential Equations pages:438-456
Conference: International Graz workshop location:Graz, Austria date:12-16 February 2001
Abstract: We deal with monogenic generalizations of the classical tangent, cotangent, secant and cosecant function constructed by generalized Eisenstein series associated with p-dimensional lattices in $R^{k+1}$, where $1 \le p \le k$. We discuss some characteristic properties of them. In particular, the generalizations of the cotangent turn out to be uniquely characterized by oddness, its principal parts and a generalized double angle formula. Further, we deduce a generalization of the classical Herglotz Lemma to Clifford analysis stating that every function which is a monogenic in a sufficiently large ball is a constant provided it satisfies the generalized cotangent double angle formula. Moreover, we show that an arbitrary $p$-fold periodic meromorphic function in $R^{k+1}$ can be represented modulo an entire function by a finite sum of the generalized cotangent functions and their partial derivatives.
ISBN: 981-02-4764-8
Publication status: published
KU Leuven publication type: IHb
Appears in Collections:Analysis Section

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