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March, 2005 Clifford and Harmonic Analysis on Cylinders and Tori
Rolf Sören Krausshar, John Ryan
Rev. Mat. Iberoamericana 21(1): 87-110 (March, 2005).


Cotangent type functions in $\mathbb{R}^n$ are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds $\mathbb{R}^n / \mathbb{Z}^k$ where $1\leq k\leq n$. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this context. Also the analogues of Calderón-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.


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Rolf Sören Krausshar. John Ryan. "Clifford and Harmonic Analysis on Cylinders and Tori." Rev. Mat. Iberoamericana 21 (1) 87 - 110, March, 2005.


Published: March, 2005
First available in Project Euclid: 22 April 2005

zbMATH: 1079.30067
MathSciNet: MR2155015

Primary: 30G35‎ , 42B30 , 53C27 , 58J32

Keywords: Clifford analysis , cotangent functions , Dirac operator

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid


Vol.21 • No. 1 • March, 2005
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