Construction of Solutions of Toda Lattices by the Classical Moment Problem
摘要
Using formulas of J. Moser for 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.