The Kerzman–stein Operator for the Ellipse
نویسندگان
چکیده
We give, in the case of ellipse, a simple connection between the spectrum of the Kerzman–Stein operator and the eccentricity of the ellipse.
منابع مشابه
A Lower Estimate for the Norm of the Kerzman-stein Operator
We establish an elementary lower estimate for the norm of the Kerzman-Stein operator for a smooth, bounded domain. The estimate involves the boundary length and logarithmic capacity. The estimate is tested on model domains for which the norm is known explicitly. It is shown that the estimate is sharp for an annulus and a strip, and is asymptotically sharp for an ellipse and a wedge.
متن کاملSpectrum of the Kerzman–Stein Operator for Model Domains
For a domain Ω ⊂ C, the Kerzman-Stein operator is the skewhermitian part of the Cauchy operator acting on L(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 spi...
متن کاملNumerical Conformal Mapping of Doubly Connected Regions via the Kerzman-stein Kernel
Abstract: An integral equation method based on the Kerzman-Stein kernel for conformal mapping of smooth doubly connected regions onto an annulus A = {w : μ < |w| < 1} is presented. The theoretical development is based on the boundary integral equation for conformal mapping of doubly connected regions with Kerzman-Stein kernel derived by Razali and one of the authors [8]. However, the integral e...
متن کاملPlemelj Projection Operators over Domain Manifolds
Plemelj projection operators are introduced for spaces of square integrable functions defined over the boundaries of a class of compact real n-dimensional manifolds lying in C. These manifolds posses many properties similar to domains in R, and are consequently called domain manifolds. The key ingredients used here are techniques from both real and complex Clifford analysis. Analogues of the Ke...
متن کاملUmbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms
We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...
متن کامل