Some properties of the Sturm-Liouville operator in L_p(R)
Spectral Theory
2007-05-23 v1 Classical Analysis and ODEs
Abstract
We consider the boundary problem -y''(x)+q(x)y(x)=f(x), lim_{|x|\to\infty}y^{(i)}(x)=0, i=0,1, where f(x)\in L_p(R), p\in[1,\infty], 1\le q(x)\in L_1^{\loc}(R). For this boundary problem we obtain: 1) necessary and sufficient conditions for unique solvability and a priori properties of the solution; 2) a criterion for the resolvent to be compact in L_p(R), and some a priori properties of the spectrum.
Keywords
Cite
@article{arxiv.math/9809012,
title = {Some properties of the Sturm-Liouville operator in L_p(R)},
author = {N. A. Chernyavskaya and L. A. Shuster},
journal= {arXiv preprint arXiv:math/9809012},
year = {2007}
}
Comments
16 pages, AMS-TeX