Document Type
Article
Publication Title
Complex Variables and Elliptic Equations
Abstract
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.
First Page
478
Last Page
492
DOI
10.1080/17476933.2014.944865
Publication Date
4-3-2015
Recommended Citation
Bolt, Michael and Raich, Andrew, "The Kerzman–Stein operator for piecewise continuously differentiable regions" (2015). University Faculty Publications and Creative Works. 200.
https://digitalcommons.calvin.edu/calvin_facultypubs/200