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Abstract <p> This review paper is devoted to the study of equiconvergence issues in spectral expansionsfor Sturm–Liouville operators on a finite interval. The potential of the Sturm–Liouville operator isassumed to be a generalized function of first-order singularity. The boundary conditions areBirkhoff regular, and the special case of Dirichlet boundary conditions is studied in detail. Resultson equiconvergence in various classes of spaces are obtained, and estimates for the rate ofequiconvergence are given. Various methods for proving the theorems—both abstract andthose based on the explicit form of asymptotics for the eigenvalues and functions of theoperators—are demonstrated.</p>

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Equiconvergence Theorems for Spectral Expansions for Sturm–Liouville Operators on a Finite Interval with Potential Distributions

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • A. M. Savchuk,
  • I. V. Sadovnichaya

摘要

Abstract

This review paper is devoted to the study of equiconvergence issues in spectral expansionsfor Sturm–Liouville operators on a finite interval. The potential of the Sturm–Liouville operator isassumed to be a generalized function of first-order singularity. The boundary conditions areBirkhoff regular, and the special case of Dirichlet boundary conditions is studied in detail. Resultson equiconvergence in various classes of spaces are obtained, and estimates for the rate ofequiconvergence are given. Various methods for proving the theorems—both abstract andthose based on the explicit form of asymptotics for the eigenvalues and functions of theoperators—are demonstrated.