Contractive extension problems for matrix valued almost periodic functions of several variables

Leiba Rodman, Ilya M. Spitkovsky, Hugo J. Woerdeman

Research output: Contribution to journalArticle

Abstract

Problems of Nehari type are studied for matrix valued k-variable almost periodic Wiener functions: Find contractive k-variable almost periodic Wiener functions having prespecified Fourier coefficients with indices in a given halfspace of ℝ. We characterize the existence of a solution, give a construction of the solution set, and exhibit a particular solution that has a certain maximizing property. These results are used to obtain various distance formulas and multivariable almost periodic extensions of Sarason's theorem. In the periodic case, a generalization of Sarason's theorem is proved using a variation of the commutant lifting theorem. The main results are further applied to a model-matching problem for multivariable linear filters.

Original languageEnglish (US)
Pages (from-to)3-35
Number of pages33
JournalJournal of Operator Theory
Volume47
Issue number1
StatePublished - 2002

Keywords

  • Almost periodic matrix functions
  • Band method
  • Besikovitch space
  • Commutant lifting
  • Contractive extensions
  • Hankel operators
  • Model matching
  • Sarason's Theorem

ASJC Scopus subject areas

  • Algebra and Number Theory

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