An Inverse Problem for Sturm-Liouville Operators on the Half-line Having Bessel-type Singularity in an Interior Point

2012/11/11 by Alexey Fedoseev, Fedoseev, Alexey
Mathematics · #34A55 (Primary) 34B24 #34L05 #47E05 (Secondary) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1211.2395

openalex publication_date 2012/11/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.

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