Clifford and harmonic analysis on cylinders and torii.

Krausshar, Rolf Sören, and Ryan, John. "Clifford and harmonic analysis on cylinders and torii.." Revista Matemática Iberoamericana 21.1 (2005): 87-110. <http://eudml.org/doc/39744>.

@article{Krausshar2005,
abstract = {Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 &lt; = k ≤ M. 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.},
author = {Krausshar, Rolf Sören, Ryan, John},
journal = {Revista Matemática Iberoamericana},
keywords = {Análisis armónico; Espacios de Hardy; Algebras de Clifford; Operadores diferenciales; Operadores integrales; Kernel; Dirac operator; Clifford analysis; cotangent function},
language = {eng},
number = {1},
pages = {87-110},
title = {Clifford and harmonic analysis on cylinders and torii.},
url = {http://eudml.org/doc/39744},
volume = {21},
year = {2005},
}

TY - JOUR
AU - Krausshar, Rolf Sören
AU - Ryan, John
TI - Clifford and harmonic analysis on cylinders and torii.
JO - Revista Matemática Iberoamericana
PY - 2005
VL - 21
IS - 1
SP - 87
EP - 110
AB - Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 &lt; = k ≤ M. 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.
LA - eng
KW - Análisis armónico; Espacios de Hardy; Algebras de Clifford; Operadores diferenciales; Operadores integrales; Kernel; Dirac operator; Clifford analysis; cotangent function
UR - http://eudml.org/doc/39744
ER -