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 problemis presented. Given a decreasing sequence of positive numbers(_n)_n>1 (i.e. ₁₂₃...0), does there exist a Hankel operatorwhose sequance of singular values is (_n)_n>1? This paper isan extension of a previously published paper in which the sameapproach was taken in the case of a monotonically decreasingsequence(_n)_n>1.     

A Parametrization Approach to Infinite-Dimensional Balanced Systems and their Approximation

The problem of generalizing the concept of balanced realizationsto infinitedimensional continuous-time systems is considered.The approach taken is based on the generalization of a parametrizationof finite dimensional balanced realizations. Using semigrouptheory an existence theorem and approximation results are derived.