Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem (Q1773526)

The authors present some exact solutions \(\{\alpha_ n(t),b_ n(t)\}_{n=1}^{\infty}\) for \(t\geq 0\) to the semi-infinite Toda lattice. Such solutions are then related to the solution to the inverse spectral problem of determining the set of constants \(\{\alpha_ n(0),b_ n(0)\}_{n=1}^{\infty}\) from a set of orthogonal polynomials \(\{P_ n(x)\}_{n=0}^{\infty}\) for \(x\in \mathbb R\) or equivalently from an associated probability measure. This paper is the extension of the earlier paper [Lett. Math. Phys. 59, No. 1, 1--17 (2002; Zbl 1004.37061)] by the authors.