Ober, Raimund
(1990)
A note on a system theoretic approach to a conjecture by Peller-Khrushchev: The general case.
*IMA Journal of Mathematical Control and Information*, 7 (1), 35-45.
(doi:10.1093/imamci/7.1.35).

## Abstract

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}.

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