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Lindner, Marko : An Identification of Convolution Operators on Cones

Lindner, Marko : An Identification of Convolution Operators on Cones

Author(s):
Lindner, Marko
Title:
An Identification of Convolution Operators on Cones
Electronic source:
application/pdf
application/postscript
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2004
Mathematics Subject Classification:
47B35 [ Toeplitz operators, Hankel operators, Wiener-Hopf operators ]
47G10 [ Integral operators ]
47B38 [ Operators on function spaces ]
Abstract:
Simonenko studied properties of convolution type operators on cones in $\R^n$. The purpose of this note is to show that every convolution operator on a suitable cone in $\R^n$ or $\Z^n$ can be identified with a standard Wiener-Hopf operator, i.e. a convolution operator on $\R_+^n$ or $\Z_+^n$, respectively. We demonstrate this identification and give explicit formulae for the convolution kernels and symbols of these Wiener-Hopf operators.
Keywords:
convolution operator, Wiener-Hopf operator, Toeplitz operator, cone
Language:
English
Publication time:
7 / 2004