Journal article
Carathéodory-Toeplitz and Nehari Problems for Matrix Valued Almost Periodic Functions
Transactions of the American Mathematical Society, v 350(6), pp 2185-2227
01 Jun 1998
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.
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Details
- Title
- Carathéodory-Toeplitz and Nehari Problems for Matrix Valued Almost Periodic Functions
- Creators
- Leiba Rodman - William & MaryIlya M. Spitkovsky - William & MaryHugo J. Woerdeman - William & Mary
- Publication Details
- Transactions of the American Mathematical Society, v 350(6), pp 2185-2227
- Publisher
- American Mathematical Society
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000073784700002
- Scopus ID
- 2-s2.0-22044457991
- Other Identifier
- 991021864938904721
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- Web of Science research areas
- Mathematics