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Escribano Iglesias, M. del Carmen and Gonzalo Palomar, Raquel and Torrano Gimenez, Emilio (2019). A dichotomy result about Hessenberg matrices associated with measures in the unit circle. "Mathematical Methods in the Applied Sciences", v. 42 (n. 17); pp. 5845-5855. ISSN 0170-4214. https://doi.org/10.1002/mma.5716.
Title: | A dichotomy result about Hessenberg matrices associated with measures in the unit circle |
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Author/s: |
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Item Type: | Article |
Título de Revista/Publicación: | Mathematical Methods in the Applied Sciences |
Date: | 2019 |
ISSN: | 0170-4214 |
Volume: | 42 |
Subjects: | |
Freetext Keywords: | Hermitian positive matrices, Compact perturbation, Hessenberg matrices, Orthogonal polynomial |
Faculty: | E.T.S. de Ingenieros Informáticos (UPM) |
Department: | Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones |
Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
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We characterize Hessenberg matrices D associated with measures in the unit circle ν, which are matrix representations of compact and actually Hilbert Schmidt perturbations of the forward shift operator as those with recursion coefficients urn:x wiley:mma:media:mma5716:mma5716-math-0001 verifying urn:x-wiley:mma:media:mma5716:mma5716-math-0002, ie, associated with measures verifying Szegö condition. As a consequence, we obtain the following dichotomy result for Hessenberg matrices associated with measures in the unit circle: either D=SR+K2 with K2, a Hilbert Schmidt matrix, or there exists an unitary matrix U and a diagonal matrix Λ such that urn:x-wiley:mma:media:mma5716:mma5716-math-0003 with K2, a Hilbert Schmidt matrix. Moreover, we prove that for 1 ≤ p ≤ 2, if urn:x-wiley:mma:media:mma5716:mma5716-math-0004, then D=SR+Kp with Kp an absolutely p summable matrix inducing an operator in the p Schatten class. Some applications are given to classify measures on the unit circle.
Type | Code | Acronym | Leader | Title |
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Government of Spain | MTM2016-80582-R | Unspecified | Universidad Politécnica de Madrid | Topología digital y matrices infinitas: aplicaciones al procesamiento de imágenes digitales |
Item ID: | 67092 |
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DC Identifier: | https://oa.upm.es/67092/ |
OAI Identifier: | oai:oa.upm.es:67092 |
DOI: | 10.1002/mma.5716 |
Official URL: | https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.5716 |
Deposited by: | Memoria Investigacion |
Deposited on: | 17 May 2021 07:57 |
Last Modified: | 17 May 2021 07:57 |