An inverse spectral problem for second-order functional-differential pencils with two delays

2020/10/27 by Sergey Buterin, Buterin, S. A., M.A. Malyugina +3 · 2 citations
Mathematics · #34A55 34B07 34K29 #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2010.14238

openalex publication_date 2020/10/27 · openalex created_date 2020/11/09 · openalex updated_date 2026/08/01

Abstract

We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary condition. The uniqueness theorem is proved and a constructive procedure for solving this inverse problem along with necessary and sufficient conditions for its solvability is obtained. Moreover, we give a survey on the contemporary state of the inverse spectral theory for operators with delay. The pencil under consideration generalizes Sturm-Liouville-type operators with delay, which allows us to illustrate essential results in this direction, including recently solved open questions.

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• Spectral properties of Schrödinger operator with translations and Neumann boundary conditions
• On non-uniqueness of recovering Sturm-Liouville operators with delay and the Neumann boundary condition at zero

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