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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the existence of eigenvalues of Toeplitz operators on planar regions


Authors: Cyrus P. Aryana and Kevin F. Clancey
Journal: Proc. Amer. Math. Soc. 132 (2004), 3007-3018
MSC (2000): Primary 47B35
Published electronically: June 2, 2004
MathSciNet review: 2063122
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Abstract: A study is made of the eigenvalues of self-adjoint Toeplitz operators on multiply connected planar regions having $g$ holes. The presence of eigenvalues is detected through an analysis of the zeros of translations of theta functions restricted to $\mathbb{R}^{g}$ in $\mathbb{C}^{g}$.


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Additional Information

Cyrus P. Aryana
Affiliation: Department of Mathematical Sciences, Saginaw Valley State University, University Center, Michigan 48710
Email: aryana@svsu.edu

Kevin F. Clancey
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: k.clancey@louisville.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07273-9
PII: S 0002-9939(04)07273-9
Keywords: Double, harmonic measure, theta function, Hardy space, Toeplitz operator
Received by editor(s): June 5, 2002
Received by editor(s) in revised form: March 7, 2003
Published electronically: June 2, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society