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Full-Text Articles in Applied Mathematics
Spectrum Of The Kerzman-Stein Operator For A Family Of Smooth Regions In The Plane, Michael Bolt
Spectrum Of The Kerzman-Stein Operator For A Family Of Smooth Regions In The Plane, Michael Bolt
University Faculty Publications and Creative Works
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 …
Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt
Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt
University Faculty Publications and Creative Works
Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.
Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt
Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt
University Faculty Publications and Creative Works
Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.