On recovering quadratic pencils with singular coefficients and entire functions in the boundary conditions

2021/11/10 by M. M. Kuznetsova, Kuznetsova, Maria · 1 citation
Mathematics · #34A55 #34B05 #34B24 #Algebraic and Geometric Analysis #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2111.05831

openalex publication_date 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering the pencil if this subspectrum generates a complete functional system. As well, we obtain an algorithm solving the inverse problem and alternative conditions on the subspectrum. Finally, these results are applied to studying a partial inverse problem.

Cited by

• Operator-differential expressions: regularization and completeness of the root functions

Related

• Partial inverse problems for quadratic differential pencils on a graph\n with a loop
• An inverse problem for the quadratic pencil of non-self-adjoint matrix\n operators on the half-line
• On a new inverse spectral problem
• An inverse problem for the matrix quadratic pencil on a finite interval
• Solvability and stability of the inverse problem for the quadratic differential pencil