Eigenvalues of the fractional Laplace operator in the interval
Spectral Theory
2010-12-07 v1 Probability
Abstract
Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional fractional Laplace operator (-d^2/dx^2)^(alpha/2) (0 < alpha < 2) in the interval (-1,1) is given: the n-th eigenvalue is equal to (n pi/2 - (2 - alpha) pi/8)^alpha + O(1/n). Simplicity of eigenvalues is proved for alpha in [1, 2). L^2 and L^infinity properties of eigenfunctions are studied. We also give precise numerical bounds for the first few eigenvalues.
Keywords
Cite
@article{arxiv.1012.1133,
title = {Eigenvalues of the fractional Laplace operator in the interval},
author = {Mateusz Kwaśnicki},
journal= {arXiv preprint arXiv:1012.1133},
year = {2010}
}
Comments
16 pages, 4 tables