UM
Adaptive orthonormal systems for matrix-valued functions
Daniel Alpay1; Fabrizio Colombo2; Tao Qian3; Irene Sabadini2
2017
Source PublicationProceedings of the American Mathematical Society
ISSN1088-6826
Volume145Issue:5Pages:2089-2106
Abstract

In this paper we consider functions in the Hardy space H defined in the unit disc of matrix-valued functions. We show that it is possible, as in the scalar case, to decompose those functions as linear combinations of suitably modified matrix-valued Blaschke products, in an adaptive way. The procedure is based on a generalization to the matrix-valued case of the maximum selection principle which involves not only selections of suitable points in the unit disc but also suitable orthogonal projections. We show that the maximum selection principle gives rise to a convergent algorithm. Finally, we discuss the case of real-valued signals.

KeywordAdaptive Decomposition Matrix-valued Blaschke Products Matrix-valued Functions And Hardy Spaces Maximum Selection Principle
DOI10.1090/proc/13359
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000395809900025
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Cited Times [WOS]:7   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorDaniel Alpay
Affiliation1.Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
2.Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133 Milano, Italy
3.Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau
Recommended Citation
GB/T 7714
Daniel Alpay,Fabrizio Colombo,Tao Qian,et al. Adaptive orthonormal systems for matrix-valued functions[J]. Proceedings of the American Mathematical Society,2017,145(5):2089-2106.
APA Daniel Alpay,Fabrizio Colombo,Tao Qian,&Irene Sabadini.(2017).Adaptive orthonormal systems for matrix-valued functions.Proceedings of the American Mathematical Society,145(5),2089-2106.
MLA Daniel Alpay,et al."Adaptive orthonormal systems for matrix-valued functions".Proceedings of the American Mathematical Society 145.5(2017):2089-2106.
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