Title: Hilbert Spaces of Solutions to Polynomial Dirac Equations, Fourier Transforms and Reproducing Kernel Functions for Cylindrical Domains
Authors: Constales, Denis
Krausshar, Rolf Sören # ×
Issue Date: Sep-2005
Publisher: Heldermann Verlag
Series Title: Zeitschrift für Analysis und ihre Anwendungen vol:24 issue:3 pages:611-636
Abstract: In this paper, we consider $L^2$ spaces of functions that satisfy polynomial Dirac equations. Fourier transformation methods and methods from harmonic analysis are then applied to treat Hilbert spaces of Clifford algebra valued functions that are either square-integrable over a cylinder or square-integrable over its boundary, and which satisfy in its interior the generalized Cauchy-Riemann system. In particular, explicit representation formulas for the Bergman and Szeg\"o reproducing kernel of several types of cylindrical domains are developed.
ISSN: 0232-2064
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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