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On the spectral character of Toeplitz operators on planar regions
Author(s):
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  -holed planar region is given via reproducing kernels in terms of theta functions on  . 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.
References:
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Additional Information:
Gholamreza
Akbari
Estahbanati
Affiliation:
Department of Mathematics and Computer Science, North Georgia College, Dahlonega, Georgia 30597
Email:
akbari@nugget.ngc.peachnet.edu
DOI:
10.1090/S0002-9939-96-03323-0
PII:
S 0002-9939(96)03323-0
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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