Indefinite Sturm--Liouville problem for some classes of self-similar singular weights

I. A. Sheipak; A. A. Vladimirov

Indefinite Sturm--Liouville problem for some classes of self-similar singular weights

Functional Analysis 2007-05-23 v1

Authors: I. A. Sheipak , A. A. Vladimirov

Abstract

We study the Sturm-Liouville problem $-y''-\rho y=0$ , $y(0)=y(1)=0$ . $\rho$ is a generalized derivative of function $P\in L_2[0,1]$ . For self-similar $P$ asymptotic formulas for eigenvalues are obtained. In this paper we consider two cases of self-similarity of $P$ : 1) arithmetic degenerate, and 2) non-arithmetic.

Keywords

sturm-liouville problem self-similar weights singular weights eigenvalues asymptotic formulas

Cite

@article{arxiv.math/0507017,
  title  = {Indefinite Sturm--Liouville problem for some classes of self-similar singular weights},
  author = {I. A. Sheipak and A. A. Vladimirov},
  journal= {arXiv preprint arXiv:math/0507017},
  year   = {2007}
}

Comments

11 pages, 1 table

Related papers

View all related →