Recovering the characteristic functions of the Sturm-Liouville differential operators with singular potentials on star-type graph with cycle

TL;DR

This paper investigates Sturm-Liouville operators with singular potentials on star-type graphs with cycles, deriving eigenvalue asymptotics and methods to recover their characteristic functions, advancing inverse spectral theory on complex graph structures.

Contribution

It introduces a novel approach to recover characteristic functions of Sturm-Liouville operators with singular potentials on star-type graphs with cycles.

Findings

Eigenvalue asymptotics for the operators are derived.

A method for recovering the characteristic function is developed.

Results extend inverse spectral theory to complex graph structures.

Abstract

We consider Sturm-Liouville operators with singular potentials from the class on star-type graph with cycle, which consist the edges with commensurable lengths. Asymptotic representation for eigenvalues for such operators is obtained. Recovering of the characteristic function the Sturm-Liouville operators with the singular potentials is considered.