Construction of solutions of Toda lattices by the classical moment problem

TL;DR

This paper develops a method to construct solutions for semi-infinite Toda lattices using classical moment problem theory, extending the applicability to a broad class of unbounded initial data.

Contribution

It introduces a novel approach linking Toda lattice solutions with the classical moment problem, enabling solutions for unbounded initial conditions.

Findings

Derived evolution law for spectral measure moments

Constructed solutions for semi-infinite Toda lattices

Extended solution methods to unbounded initial data

Abstract

Making use of formulas of J. Moser for a finite-dimensional Toda lattices, we derive the evolution law for moments of the spectral measure of the semi-infinite Jacobi operator associated with the Toda lattice. This allows us to construct solutions of semi-infinite Toda lattices for a wide class of unbounded initial data by using well-known results from the classical moment problem theory.