The Carathéodory-Toeplitz problem for almost periodic functions

Ilya M. Spitkovsky; Hugo J. Woerdeman

doi:10.1006/jfan.1993.1091

The Carathéodory-Toeplitz problem for almost periodic functions

Ilya M. Spitkovsky, Hugo J. Woerdeman

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	281-293
Number of pages	13
Journal	Journal of Functional Analysis
Volume	115
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1993.1091
State	Published - Aug 1 1993

ASJC Scopus subject areas

Analysis

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10.1006/jfan.1993.1091

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abstract = "In this paper we consider the Carath{\'e}odory-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.",

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The Carathéodory-Toeplitz problem for almost periodic functions

Abstract

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