On the spectral character of Toeplitz operators on multiply connected domains

Clancey, Kevin F.

doi:10.1090/S0002-9947-1991-1012524-6

On the spectral character of Toeplitz operators on multiply connected domains
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by Kevin F. Clancey

Trans. Amer. Math. Soc. 323 (1991), 897-910

DOI: https://doi.org/10.1090/S0002-9947-1991-1012524-6

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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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