On the spectral character of Toeplitz operators on planar regions

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 kern...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1996-09, Vol.124 (9), p.2737-2744
Main Author: Estahbanati, Gholamreza Akbari
Format: Article
Language:English
Subjects:
Analytic functions
Connected regions
Mathematical functions
Meromorphic functions
Riemann surfaces
Simply connected regions
Spectral theory
Symbolism
Symbols
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-96-03323-0