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Journal of Mathematical Analysis and Applications


The Kerzman-Stein operator is the skew-hermitian part of the Cauchy operator defined with respect to an unweighted hermitian inner product on the boundary. For bounded regions with smooth boundary, the Kerzman-Stein operator is compact on the Hilbert space of square integrable functions. Here we give an explicit computation of its Hilbert-Schmidt norm for a family of simply connected regions. We also give an explicit computation of the Cauchy operator acting on an orthonormal basis, and we give estimates for the norms of the Kerzman-Stein and Cauchy operators on these regions. The regions are the first regions that display no apparent Möbius symmetry for which there now is explicit spectral information.

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