Uniform asyptotic formulae for eigenfunctions of Sturm--Liouville operators with singular potentials

2008/01/13 by A. M. Savchuk, А. М. Савчук, Savchuk, A. M.
Engineering · Mathematics · Physics and Astronomy · #34L20 #47e05 #FOS: Mathematics #Functional Analysis (math.FA) #Material Science and Thermodynamics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:34L20 #msc:47e05

paper · pdf · doi:10.48550/arxiv.0801.1950

8 pages

arxiv created 2008/01/13 · openalex publication_date 2008/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study a Sturm--Liouville operator Ly=-y''+q(x)y in the space L₂[0,π] with Direchlet boundary conditions. Here the potential q is a fitst order distribution q∈ W₂^-1[0,π]. Such operators were defined in our previous papers. Here we study an asymptotic behaviour of eigenfunctions with uniform estimates of rests. We obtain this estimates also for potentials from Sobolev spaces q∈ W₂^θ-1, where θ∈[0,1/2).

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