Adaptive orthonormal systems for matrix-valued functions
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- by Daniel Alpay, Fabrizio Colombo, Tao Qian and Irene Sabadini PDF
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Abstract:
In this paper we consider functions in the Hardy space $\mathbf {H}_2^{p\times q}$ 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.References
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Additional Information
- Daniel Alpay
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
- MR Author ID: 223612
- Email: dany@math.bgu.ac.il
- Fabrizio Colombo
- Affiliation: Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133 Milano, Italy
- MR Author ID: 601509
- Email: fabrizio.colombo@polimi.it
- Tao Qian
- Affiliation: Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau
- MR Author ID: 208864
- Email: fsttq@umac.mo
- Irene Sabadini
- Affiliation: Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133 Milano, Italy
- MR Author ID: 361222
- Email: irene.sabadini@polimi.it
- Received by editor(s): May 1, 2016
- Received by editor(s) in revised form: June 30, 2016
- Published electronically: January 6, 2017
- Communicated by: Stephan Ramon Garcia
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2089-2106
- MSC (2010): Primary 47A56, 41A20, 30H10
- DOI: https://doi.org/10.1090/proc/13359
- MathSciNet review: 3611323