Formulas for Singular Values of Hankel Operators and Mixed Hankel-Toeplitz Operators Using Lifting Technique on the Left Shift Invariant Subspace

Abstract

This paper derives Hamiltonian formulas for singular values of Hankel operators and mixed Hankel-Toeplitz operators. Given an inner function and a continuous time linear system, it is shown that there is a discrete-time linear system whose input-output space is the left shift invariant subspace associated to the inner function. Using this lifting technique, a Schmidt pair of the operators are characterized as a solution to a discrete-time two-point boundary value problem. This results in a transcendental equation for singular values.