Spectrum of the Kerzman-Stein operator for a family of smooth regions in the plane

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Bolt, Michael

关键词: Kerzman-Stein operator;    Cauchy operator;    Hilbert-Schmidt norm;   

DOI  :  10.1016/j.jmaa.2013.11.049

来源: Elsevier

【 摘 要 】

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 HilbertSchmidt 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 Mobius symmetry for which there now is explicit spectral information. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free