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On the spectral character of Toeplitz operators on multiply connected domains

Author: Kevin F. Clancey
Journal: Trans. Amer. Math. Soc. 323 (1991), 897-910
MSC: Primary 47B35; Secondary 30D55
MathSciNet review: 1012524
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Abstract: An explicit resolvent formula is given for selfadjoint Toeplitz operators acting on the least harmonic majorant Hardy spaces of a multiply connected planar domain. This formula is obtained by using theta functions associated with the double of the domain. Several consequences concerning the spectral resolutions of selfadjoint Toeplitz operators are deduced.

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Article copyright: © Copyright 1991 American Mathematical Society

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