Fredholm Eigenvalue for a Quasi-circle and Grunsky Functionals
نویسنده
چکیده
We give several new formulas of the least positive Fredholm eigenvalue for a quasicircle, answering a problem posed recently by Kühnau. During the proof, we show that the Grunsky functionals corresponding to the two complementary domains of the quasi-circle are the same and equal to the reciprocal of the Fredholm eigenvalue.
منابع مشابه
The Quasi-Random Walk
We present the method of the quasi-random walk for the approximation of functionals of the solution of second kind Fredholm integral equations. This deterministic approach efficiently uses low discrepancy sequences for the quasi-Monte Carlo integration of the Neumann series. The fast procedure is illustrated in the setting of computer graphics, where it is applied to several aspects of the glob...
متن کاملPolynomial perturbations of hermitian linear functionals and difference equations
This paper is devoted to the study of general (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial modifications of arbitrary degree. The main objective is the characterization of the quasi-definiteness of the functionals involved in the problem in terms of a ...
متن کاملConvergence Analysis of a Galerkin Boundary Element Method for the Dirichlet Laplacian Eigenvalue Problem
In this paper, a rigorous convergence and error analysis of a Galerkin boundary element method for the Dirichlet Laplacian eigenvalue problem is presented. The formulation of the eigenvalue problem in terms of a boundary integral equation yields a nonlinear boundary integral operator eigenvalue problem. This nonlinear eigenvalue problem and its Galerkin approximation are analyzed in the framewo...
متن کاملWeil-petersson Metric on the Universal Teichmüller Space Ii. Kähler Potential and Period Mapping
We study the Hilbert manifold structure on T0(1) — the connected component of the identity of the Hilbert manifold T (1). We characterize points on T0(1) in terms of Bers and pre-Bers embeddings, and prove that the Grunsky operators B1 and B4, associated with the points in T0(1) via conformal welding, are Hilbert-Schmidt. We define a “universal Liouville action” — a real-valued function S1 on T...
متن کاملMachine Learning and Integral Equations
As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering. In analogy to recent advances in reinforcement learning for p...
متن کامل