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

A note on a system theoretic approach to a conjecture by Peller-Khrushchev: The general case
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 (σn)n>1 (i.e. σ1≥σ2≥σ3≥... ≥0), does there exist a Hankel operator whose sequance of singular values is (σn)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(σn)n>1.

0265-0754
35-45
Ober, Raimund
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Ober, Raimund
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

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).

Record type: Article

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 (σn)n>1 (i.e. σ1≥σ2≥σ3≥... ≥0), does there exist a Hankel operator whose sequance of singular values is (σn)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(σn)n>1.

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Published date: 1 March 1990

Identifiers

Local EPrints ID: 424998
URI: https://eprints.soton.ac.uk/id/eprint/424998
ISSN: 0265-0754
PURE UUID: 99c27f68-68ab-4df8-ac38-701e633d05e0
ORCID for Raimund Ober: ORCID iD orcid.org/0000-0002-1290-7430

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Date deposited: 09 Oct 2018 16:30
Last modified: 14 Mar 2019 01:21

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