Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions

M. A. Kaashoek; F. van Schagen

doi:10.1007/978-3-030-10850-2_13

Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions

M. A. Kaashoek^*, F. van Schagen

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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Abstract

The theory of onefold and twofold Ellis-Gohberg inverse problems for Wiener functions on the real line is specified further for the scalar case. Assuming the left onefold problem or the right onefold problem to be solvable, a necessary and sufficient condition is given for the twofold problem to be solvable. In that case the left and the right onefold problem are both solvable, and the solutions are equal. An example shows that the latter is not always true, i.e., the left and the right onefold problem are solvable does not imply that the solutions are equal.

Original language	English
Title of host publication	Positivity and Noncommutative Analysis
Subtitle of host publication	Festschrift in Honour of Ben de Pagteron the Occasion of his 65th Birthday
Editors	Gerard Busker, Marcel de Jeu, Peter Dodds, Anton Schep, Fedor Sukochev, Jan van Neerven, Anthony Wickstead
Publisher	Springer International Publishing AG
Pages	257-267
Number of pages	11
ISBN (Electronic)	9783030108502
ISBN (Print)	9783030108496
DOIs	https://doi.org/10.1007/978-3-030-10850-2_13
Publication status	Published - 2019

Publication series

Name	Trends in Mathematics
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Keywords

Hankel operator
Inner-outer factorization
Inverse problem for orthogonal functions
Rational functions
Realization
Toeplitz operator
Wiener algebra

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10.1007/978-3-030-10850-2_13

Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class FunctionsFinal published version, 219 KBLicence: Article 25fa Dutch Copyright Act

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Kaashoek, M. A., & van Schagen, F. (2019). Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions. In G. Busker, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven, & A. Wickstead (Eds.), Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagteron the Occasion of his 65th Birthday (pp. 257-267). (Trends in Mathematics). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-10850-2_13

Kaashoek, M. A. ; van Schagen, F. / Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions. Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagteron the Occasion of his 65th Birthday. editor / Gerard Busker ; Marcel de Jeu ; Peter Dodds ; Anton Schep ; Fedor Sukochev ; Jan van Neerven ; Anthony Wickstead. Springer International Publishing AG, 2019. pp. 257-267 (Trends in Mathematics).

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abstract = "The theory of onefold and twofold Ellis-Gohberg inverse problems for Wiener functions on the real line is specified further for the scalar case. Assuming the left onefold problem or the right onefold problem to be solvable, a necessary and sufficient condition is given for the twofold problem to be solvable. In that case the left and the right onefold problem are both solvable, and the solutions are equal. An example shows that the latter is not always true, i.e., the left and the right onefold problem are solvable does not imply that the solutions are equal.",

keywords = "Hankel operator, Inner-outer factorization, Inverse problem for orthogonal functions, Rational functions, Realization, Toeplitz operator, Wiener algebra",

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Kaashoek, MA & van Schagen, F 2019, Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions. in G Busker, M de Jeu, P Dodds, A Schep, F Sukochev, J van Neerven & A Wickstead (eds), Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagteron the Occasion of his 65th Birthday. Trends in Mathematics, Springer International Publishing AG, pp. 257-267. https://doi.org/10.1007/978-3-030-10850-2_13

Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions. / Kaashoek, M. A.; van Schagen, F.
Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagteron the Occasion of his 65th Birthday. ed. / Gerard Busker; Marcel de Jeu; Peter Dodds; Anton Schep; Fedor Sukochev; Jan van Neerven; Anthony Wickstead. Springer International Publishing AG, 2019. p. 257-267 (Trends in Mathematics).

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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AB - The theory of onefold and twofold Ellis-Gohberg inverse problems for Wiener functions on the real line is specified further for the scalar case. Assuming the left onefold problem or the right onefold problem to be solvable, a necessary and sufficient condition is given for the twofold problem to be solvable. In that case the left and the right onefold problem are both solvable, and the solutions are equal. An example shows that the latter is not always true, i.e., the left and the right onefold problem are solvable does not imply that the solutions are equal.

KW - Hankel operator

KW - Inner-outer factorization

KW - Inverse problem for orthogonal functions

KW - Rational functions

KW - Realization

KW - Toeplitz operator

KW - Wiener algebra

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Kaashoek MA, van Schagen F. Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions. In Busker G, de Jeu M, Dodds P, Schep A, Sukochev F, van Neerven J, Wickstead A, editors, Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagteron the Occasion of his 65th Birthday. Springer International Publishing AG. 2019. p. 257-267. (Trends in Mathematics). Epub 2019 Aug 10. doi: 10.1007/978-3-030-10850-2_13

Onefold and Twofold Ellis–Gohberg Inverse Problems for Scalar Wiener Class Functions

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