Spectrum of the Kerzman?Stein Operator for Model Domains

Abstract

For a domain Ω ⊂ C, the Kerzman-Stein operator is the skew- hermitian part of the Cauchy operator acting on L 2 (bΩ), which is defined with respect to Euclidean measure. In this paper we compute the spectrum of the Kerzman-Stein operator for three domains whose boundaries consist of two circular arcs: a strip, a wedge, and an annulus. We also treat the case of a domain bounded by two logarithmic spirals.