On the spectral character of Toeplitz operators on planar regions

Estahbanati, Gholamreza

doi:10.1090/S0002-9939-96-03323-0

On the spectral character of Toeplitz operators on planar regions
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by Gholamreza Akbari Estahbanati

Proc. Amer. Math. Soc. 124 (1996), 2737-2744

DOI: https://doi.org/10.1090/S0002-9939-96-03323-0

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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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