Perturbed eigenvalue problems: an overview

نویسندگان

چکیده

The study of perturbed eigenvalue problems has been a very active field investigation throughout the years. In this survey we collect several results in field.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The integral equation methods for the perturbed Helmholtz eigenvalue problems

It is well known that the main difficulty in solving eigenvalue problems under shape deformation relates to the continuation of multiple eigenvalues of the unperturbed configuration. These eigenvalues may evolve, under shape deformation, as separated, distinct eigenvalues. In this paper, we address the integral equation method in the evaluation of eigenfunctions and the corresponding eigenvalue...

متن کامل

Inverse Eigenvalue Problems for Perturbed Spherical Schrödinger Operators

We investigate the eigenvalues of perturbed spherical Schrödinger operators under the assumption that the perturbation q(x) satisfies xq(x) ∈ L1(0, 1). We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to an decaying error depending on the behavior of q(x) near x = 0. Furthermore, we provide sets of spectral data which uniquely determin...

متن کامل

Eigenvalue Estimates for the Perturbed Andersson Model

Consider the operator H = −∆ + pω − V, where pω is the potential of the Andersson type and V ≥ 0 is a function that decays slowly at the infinity. We study the rate of accumulation of eigenvalues of H to the bottom of the essential spectrum. 1. STATEMENT OF THE MAIN RESULT The question we study is rooted in two different areas of mathematics: the spectral theory of differential operators and th...

متن کامل

An Arnoldi Method for Nonlinear Eigenvalue Problems

For the nonlinear eigenvalue problem T (λ)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem gover...

متن کامل

Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization

In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on the preconditioned inverse iteration (PINVIT) for matrices [Knyazev and Neymeyr, (2009)] is extended to the case of operators. We show that convergence is retained up to any tolerance if one only uses approximate ap...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Studia Universitatis Babe?-Bolyai

سال: 2021

ISSN: ['1224-8754', '2065-9458']

DOI: https://doi.org/10.24193/subbmath.2021.1.05