For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for such problems. In this study, from an analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we provide a novel interpretation of ...

The paper is devoted to first-order trace formulas for the iterates of the Fox–Li and related Wiener–Hopf integral operators. Such formulas provide first insight into the asymptotic behaviour of the eigenvalues and can be used to test whether a specific guess for the eigenvalue distribution is acceptable or not. The main technical problem consists in obtaining the asymptotics of a multivariate ...

We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. discuss the analytic properties of discretisation, outline implementation, showcase numerical examples.

Spurious eigensolutions in the boundary integral equation (BIE) or boundary element method (BEM) for doublyconnected domain problems, the eccentric and annular membranes, are studied analytically and numerically in this paper. For the mathematical analysis, we employ the null-field integral equation, the degenerate kernels and the Fourier series to prove the existence of spurious eigensolutions...

The foundation of the beam perturbation formalism was established on the Sacherer integral equation [1]. The original solution was obtained by using simplified radial functions, and the results can be used to explain several important beam instability problems. To solve the instabilities caused by high beam intensities calls for more complete solution and the extension to the formalism as well....

Abstract We compute the leading coefficient in asymptotic expansion of eigenvalue counting function for Kohn Laplacian on spheres. express as an infinite sum and integral.

The norm of an integral operator occurring in the partial wave decomposition of an operator B introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that B is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a speciied critical value.

appear (the uj run over an orthonormal basis of automorphic Laplaceeigenforms), so our formula (Theorem 1) is a duality between such integrals and certain geodesic integrals of u. New integral transformations are involved depending on the Laplace-eigenvalue of u. We invert these integral transformations in Section 5, Theorem 2. We develop the formula for finite volume Fuchsian groups, so (as in...

abstract Lanczos's major contributions to the numerical solution of linear equations are contained in two papers: \An Iteration Method for the Solution of the Eigenvalue Problem of Linear Diierential and Integral Operators" and \Solutions of Linear Equations by Minimized Iterations ," the second of which contains the method of conjugate gradients. In this note we retrace Lanczos's journey from ...