An inverse problem for the matrix quadratic pencil on a finite interval

2013/01/13 by Natalia P. Bondarenko, Bondarenko, Natalia
Computer Science · Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1301.2760

openalex publication_date 2013/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a quadratic matrix boundary value problem with equations and boundary conditions dependent on a spectral parameter. We study an inverse problem that consists in recovering the differential pencil by the so-called Weyl matrix. We obtain asymptotic formulas for the solutions of the considered matrix equation. Using the ideas of the method of spectral mappings, we prove the uniqueness theorem for this inverse problem.

Citations

• Reconstruction of energy-dependent Sturm-Liouville equations from two\n spectra

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