This article is cited in 7 papers

Mathematics

Spectral characteristics of the Sturm–Liouville operator under minimal restrictions on smoothness of coefficients

V. E. Vladykina

Lomonosov Moscow State University, Faculty of Cosmic Research

Abstract: In this paper we consider the Sturm–Liouville problem in general form with Dirichlet boundary conditions under the minimal smoothness assumptions for the coefficients. We obtain the asymptotics formulas for eigenvalues and eigenfunctions of this problem. In assumption that $L^p$-norm of eigenfunctions is equal to 1, we get uniform estimates of the Chebyshev norm.

Key words: the Sturm–Liouville equation, asymptotics of the eigenvalues, asymptotics of the eigenfunctions, singular coefficients.

UDC: 517.928+517.984

Received: 12.04.2019

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2019, 74:6, 235–240

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