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Related papers: Transmission eigenvalues for elliptic operators

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In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is…

Functional Analysis · Mathematics 2019-03-26 M. V. Kukushkin

In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in…

Spectral Theory · Mathematics 2009-12-02 Johannes Sjoestrand

We consider $C=A+B$ where $A$ is selfadjoint with a gap $(a,b)$ in its spectrum and $B$ is (relatively) compact. We prove a general result allowing $B$ of indefinite sign and apply it to obtain a $(\delta V)^{d/2}$ bound for perturbations…

Spectral Theory · Mathematics 2015-05-13 Dirk Hundertmark , Barry Simon

The paper is concerned with the principal eigenvalue of some linear elliptic operators with drift in two dimensional space. We provide a refined description of the asymptotic behavior for the principal eigenvalue as the drift rate…

Analysis of PDEs · Mathematics 2024-05-17 Shuang Liu , Yuan Lou , Maolin Zhou

We study the location of the transmission eigenvalues in the isotropic case when the restrictions of the refraction indices on the boundary coincide. Under some natural conditions we show that there exist parabolic transmission…

Analysis of PDEs · Mathematics 2017-02-14 Georgi Vodev

The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic and homogenous. In particular we prove maximum and comparison principle, Holder…

Analysis of PDEs · Mathematics 2007-05-23 I. Birindelli , F. Demengel

We introduce a new class of natural, explicitly defined, transversally elliptic differential operators over manifolds with compact group actions. Under certain assumptions, the symbols of these operators generate all the possible values of…

Differential Geometry · Mathematics 2021-01-28 Igor Prokhorenkov , Ken Richardson

We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…

Numerical Analysis · Mathematics 2018-07-10 Peter Kritzer , Henryk Wozniakowski

In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, \, \mu,…

Analysis of PDEs · Mathematics 2020-05-01 Fioralba Cakoni , Hoai-Minh Nguyen

We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…

Mathematical Physics · Physics 2007-05-23 Olaf Post

We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, starting with the standard bidomain mathematical model related…

Analysis of PDEs · Mathematics 2021-06-09 Alexander Shlapunov , Yulia Shefer

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the…

Probability · Mathematics 2012-06-25 Mu-Fa Chen , Ling-Di Wang , Yu-Hui Zhang

Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T…

Statistical Mechanics · Physics 2007-09-24 Klaus Fabricius , Barry M. McCoy

A basic problem in operator theory is to estimate how a small perturbation effects the eigenspaces of a self-adjoint compact operator. In this paper, we prove upper bounds for the subspace distance, taylored for structured random…

Probability · Mathematics 2018-12-18 Moritz Jirak , Martin Wahl

We study an eigenvalue problem for functions in R^N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear…

Analysis of PDEs · Mathematics 2010-12-30 Jacopo Bellazzini , Vieri Benci , Marco G. Ghimenti , A. M. Micheletti

We use variational methods to derive Hadamard-type formulae for the eigenvalues of a class of elliptic operators on a compact Riemannian manifold $M$. We then apply the latter in the following context. Consider a family of elliptic…

Differential Geometry · Mathematics 2023-06-13 Cleiton Lira Cunha , José Nazareno Vieira Gomes , Marcus Antônio Mendonça Marrocos

The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…

Functional Analysis · Mathematics 2022-03-31 Nigar Aslanova , Kh. Aslanov

We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.

Spectral Theory · Mathematics 2008-02-19 Michael Demuth , Marcel Hansmann , Guy Katriel

In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…

Numerical Analysis · Mathematics 2025-10-08 Nicolás A. Barnafi , Felipe Lepe , Francisca Muñoz Riquelme

We study discrete Schroedinger operators with compactly supported potentials on the square lattice. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely…

Spectral Theory · Mathematics 2011-09-14 Hiroshi Isozaki , Evgeny Korotyaev