Adaptive orthonormal systems for matrix-valued functions

Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In this paper we consider functions in the Hardy space Hp×q2 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.

Original languageEnglish
Pages (from-to)2089-2106
Number of pages18
JournalProceedings of the American Mathematical Society
Issue number5
StatePublished - 1 Jan 2017


  • Adaptive decomposition
  • Matrix-valued Blaschke products
  • Matrix-valued functions and Hardy spaces
  • Maximum selection principle

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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