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Full-Text Articles in Applied Mathematics
The Kerzman–Stein Operator For Piecewise Continuously Differentiable Regions, Michael Bolt, Andrew Raich
The Kerzman–Stein Operator For Piecewise Continuously Differentiable Regions, Michael Bolt, Andrew Raich
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 a rectifiable curve. If the curve is continuously differentiable, the Kerzman–Stein operator is compact on the Hilbert space of square integrable functions; when there is a corner, the operator is noncompact. Here, we give a complete description of the spectrum for a finite symmetric wedge and we show how this reveals the essential spectrum for curves that are piecewise continuously differentiable. We also give an explicit construction for a smooth curve whose Kerzman–Stein operator has large norm.
Cauchy Integrals And Möbius Geometry Of Curves, David E. Barrett, Michael Bolt
Cauchy Integrals And Möbius Geometry Of Curves, David E. Barrett, Michael Bolt
University Faculty Publications and Creative Works
No abstract provided.