A note on a system theoretic approach to a conjecture by Peller-Khrushchev: The general case

Based on the construction of infinite-dimensional balanced realizations, an alternative solution to the following inverse spectral problem is presented. Given a decreasing sequence of positive numbers (σ n ) n>1 (i.e. σ 1 ≥σ 2 ≥σ 3 ≥... ≥0), does there exist a Hankel operator whose sequance of singular values is (σ n ) n>1 ? This paper is an extension of a previously published paper in which the same approach was taken in the case of a monotonically decreasing sequence(σ n ) n>1 .