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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the spectral character
of Toeplitz operators on planar regions

Author: Gholamreza Akbari Estahbanati
Journal: Proc. Amer. Math. Soc. 124 (1996), 2737-2744
MSC (1991): Primary 47B35
MathSciNet review: 1326992
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Abstract: Self-adjoint Toeplitz operators on multiply connected planar regions are investigated using theta functions on the double. An explicit resolvent form for self-adjoint Toeplitz operators on a Hardy space associated with any representing measure on a $g$-holed planar region is given via reproducing kernels in terms of theta functions on $\mathbb {C}^g$. This resolvent formula is a generalization of an analogous formula obtained by K. F. Clancey (1991) for the case of harmonic measure. Applications of this resolvent form to the spectral type of the self-adjoint Toeplitz operators are described.

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Additional Information

Gholamreza Akbari Estahbanati
Affiliation: Department of Mathematics and Computer Science, North Georgia College, Dahlonega, Georgia 30597

Keywords: Riemann surface, double, representing measure, theta function, Hardy space, Toeplitz operator
Received by editor(s): September 13, 1994
Received by editor(s) in revised form: January 30, 1995, and March 3, 1995
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society