Carathéodory-toeplitz and nehari problems for matrix valued almost periodic functions

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

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Abstract

In this paper the positive and strictly contractive extension problems for almost periodic matrix functions are treated. We present necessary and sufficient conditions for the existence of extensions in terms of Toeplitz and Hankel operators on Besicovitch spaces and Lebesgue spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property. A linear fractional parameterization of the set of all extensions is also provided. The techniques used in the proofs include factorizations of matrix valued almost periodic functions and a . general algebraic scheme called the band method.

Original languageEnglish (US)
Pages (from-to)2185-2227
Number of pages43
JournalTransactions of the American Mathematical Society
Volume350
Issue number6
StatePublished - Dec 1 1998

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Keywords

  • Almost periodic matrix functions
  • Band method
  • Besicovitch space
  • Canonical factorization
  • Contractive extensions
  • Hankel operators
  • Positive extensions
  • Toeplitz operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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