The Carathéodory-Toeplitz problem for almost periodic functions

Ilya M. Spitkovsky, Hugo J. Woerdeman

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Abstract

In this paper we consider the Carathéodory-Toeplitz positive extension problem in the Wiener algebra of almost periodic functions. We derive necessary and sufficient conditions for the existence of a positive band extension, which is also characterized by a maximum entropy principle. In addition a linear fractional parametrization for the set of all positive extensions of a given function is obtained.

Original languageEnglish (US)
Pages (from-to)281-293
Number of pages13
JournalJournal of Functional Analysis
Volume115
Issue number2
DOIs
StatePublished - Aug 1 1993

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ASJC Scopus subject areas

  • Analysis

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