Inverse spectral problem for a third-order differential operator with non-local potential

TL;DR

This paper investigates the spectral properties of a third-order differential operator with a non-local potential, providing solutions to both direct and inverse problems and introducing analogous elementary functions.

Contribution

It introduces elementary functions similar to sines and cosines for third-order operators with non-local potentials and solves the direct and inverse spectral problems.

Findings

Elementary functions analogous to sines and cosines are described.

Solutions to the direct spectral problem are provided.

Solutions to the inverse spectral problem are established.

Abstract

Spectral problem for a self-adjoint third-order differential operator with non-local potential on a finite interval is studied. Elementary functions that are analogues of sines and cosines for such operators are described. Direct and inverse problems for third-order operators with non-local potential are solved.