On Dual Canonical Systems and Dual Matrix String Equations

Abstract

A class of canonical systems and dual canonical systems which is equivalent to a class of matrix string equations and dual matrix string equations, respectively, under appropriate smoothness conditions is introduced. This serves to generalize the notion of dual string equations which was introduced by Kac and Krein for scalar strings some thirty years ago. A complete description of the set of spectral functions τ(μ) on [0, ∞) for the original mastrix string equation such that $\tilde{\tau }(\mu ) = \int_{0}^{\mu } {\lambda d\tau (\lambda )}$ is a spectral function for the dual matrix string is furnished.