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On the existence of eigenvalues of Toeplitz operators on planar regions

Author(s): Cyrus P. Aryana; Kevin F. Clancey
Journal: Proc. Amer. Math. Soc. 132 (2004), 3007-3018.
MSC (2000): Primary 47B35
Posted: June 2, 2004
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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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G. Akbari Estahbanati (Cyrus P. Aryana), Riemann surfaces and Toeplitz operators on multiply connected planar regions, Dissertation, University of Georgia, 1993.

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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: 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
Posted: June 2, 2004
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2004, American Mathematical Society

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