Title: Clifford and harmonic analysis on cylinders and tori
Authors: Krausshar, Rolf Sören ×
Ryan, John #
Issue Date: 2005
Publisher: Universidad autonoma madrid
Series Title: Revista matematica iberoamericana vol:21 issue:1 pages:87-110
Abstract: Cotangent type functions in $R^n$ are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds $R^n/Z(k)$ where $ 1 \le k \le n$. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szego kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals axe also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this context. Also the analogues of Calderon-Zygmund type operators are introduced in this context, together with singular Clifford holomorphic, or monogenic, kernels defined on sector domains in the context of cylinders. Fundamental differences in the context of the n-torus arising from a double singularity for the generalized Cauchy kernel on the torus are also discussed.
ISSN: 0213-2230
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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