Unique solvability of a coupling problem for entire functions

TL;DR

This paper proves the unique solvability of a coupling problem for entire functions, which is important for inverse spectral theory and integrating certain nonlinear wave equations.

Contribution

It establishes the first rigorous proof of unique solvability for this specific coupling problem in entire functions.

Findings

Proves unique solvability of the coupling problem.

Links the problem to inverse spectral theory.

Relevance to nonlinear wave equations integration.

Abstract

We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance for the integration of certain nonlinear wave equations.