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Lacunas in the Support of the Weyl Calculus for Two Hermitian Matrices

Part of: Topological algebras, normed rings and algebras, Banach algebras Generalized function theory General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Brian Jefferies  and
Bernd Straub
Bernd Straub
Affiliation:
School of Mathematics The University of New South Wales Sydney NSW 2052 Australia e-mail: b.jefferies@unsw.edu.au, bernd@maths.unsw.edu.au
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Abstract

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The connection between Clifford analysis and the Weyl functional calculus for a d-tuple of bounded selfadjoint operators is used to prove a geometric condition due to J. Bazer and D. H. Y. Yen for a point to be in the support of the Weyl functional calculus for a pair of hermitian matrices. Examples are exhibited in which the support has gaps.

Keywords

lacunasWeyl functional calculusClifford algebramonogenic functionsymmetric hyperbolic system.

MSC classification

Secondary: 47A60: Functional calculus 46H30: Functional calculus in topological algebras 47A25: Spectral sets 30G35: Functions of hypercomplex variables and generalized variables
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 1 , August 2003 , pp. 85 - 124
Copyright
Copyright © Australian Mathematical Society 2003

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