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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Carathéodory-Toeplitz and Nehari problems for matrix valued almost periodic functions
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by Leiba Rodman, Ilya M. Spitkovsky and Hugo J. Woerdeman PDF
Trans. Amer. Math. Soc. 350 (1998), 2185-2227 Request permission

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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Additional Information
  • Leiba Rodman
  • Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795
  • Email: lxrodm@math.wm.edu
  • Ilya M. Spitkovsky
  • Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795
  • MR Author ID: 191035
  • ORCID: 0000-0002-1411-3036
  • Email: ilya@math.wm.edu
  • Hugo J. Woerdeman
  • Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795
  • MR Author ID: 183930
  • Email: hugo@math.wm.edu
  • Received by editor(s): April 29, 1996
  • Received by editor(s) in revised form: September 18, 1996
  • Additional Notes: The research is partially supported by NSF Grants 9500924 (LR, HJW) and 9401848 (IMS). The research of IMS was also supported by a semester research grant from the College of William & Mary
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2185-2227
  • MSC (1991): Primary 42A75, 26A99, 15A54, 47A68, 47A56, 47A57, 42A82, 47B35
  • DOI: https://doi.org/10.1090/S0002-9947-98-01937-0
  • MathSciNet review: 1422908