On Quasi-periodic Differential Pencils with Jump Conditions Inside the Interval

TL;DR

This paper studies non-self-adjoint differential pencils with jump conditions, analyzing their spectral properties and solving the inverse spectral problem with a proven uniqueness theorem and a reconstruction algorithm.

Contribution

It introduces a novel analysis of spectral properties and provides a new method for solving the inverse spectral problem for these operators.

Findings

Spectral characteristics are thoroughly characterized.

A uniqueness theorem for the inverse problem is established.

An explicit algorithm for operator reconstruction is developed.

Abstract

Non-self-adjoint second-order differential pencils on a finite interval with non-separated quasi-periodic boundary conditions and jump conditions are studied. We establish properties of spectral characteristics and investigate the inverse spectral problem of recovering the operator from its spectral data. For this inverse problem we prove the corresponding uniqueness theorem and provide an algorithm for constructing its solution.