Chains of reproducing kernel Hilbert spaces generated by unimodular functions

TL;DR

This paper introduces a method to generate chains of reproducing kernel Hilbert spaces from unimodular functions, enabling solutions to inverse problems in de Branges spaces through differential equations.

Contribution

It provides a novel approach to construct RKHS chains from unimodular functions and applies it to solve inverse problems in de Branges spaces.

Findings

Method to construct RKHS chains from unimodular functions

Application to inverse problems in de Branges spaces

Solution via differential equations

Abstract

We present a method to construct a chain of reproducing kernel Hilbert spaces controlled by a first-order system of differential equations from a given unimodular function satisfying several conditions. One of the applications of that method is a conditional but richly general solution to the inverse problem of recovering the structure Hamiltonian from a given de Branges space.