Solutions of Toda lattices for semi-bounded initial data and classical moment problem

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.