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Factorization of Block Triangular Matrix Functions in Wiener Algebras on Ordered Abelian Groups

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Current Trends in Operator Theory and its Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 149))

Abstract

The notion of Wiener-Hopf type factorization is introduced in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups. Factorizations of 2 x 2 block triangular matrix functions with elementary functions on the main diagonal are studied in detail. A conjecture is formulated concerning characterization of dual groups with the property that every invertible matrix function in a Wiener algebra admits a factorization. Applications of factorization are given to systems of difference equations and orthogonal families of functions.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, Cagliari, I-09123, Italy

    Cornelis V. M. van der Mee

  2. Department of Mathematics, College of William and Mary, P. O. Box 8795 , Williamsburg, 23187-8795, VA, USA

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

  3. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001, Heverlee, Belgium

    Hugo J. Woerdeman

Authors
  1. Cornelis V. M. van der Mee
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  2. Leiba Rodman
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  3. Ilya M. Spitkovsky
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  4. Hugo J. Woerdeman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball  & Martin Klaus  & 

  2. Department of Mathematics, University of California, La Jolla, CA, 92093, USA

    J. William Helton

  3. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Leiba Rodman

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© 2004 Springer Basel AG

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van der Mee, C.V.M., Rodman, L., Spitkovsky, I.M., Woerdeman, H.J. (2004). Factorization of Block Triangular Matrix Functions in Wiener Algebras on Ordered Abelian Groups. In: Ball, J.A., Helton, J.W., Klaus, M., Rodman, L. (eds) Current Trends in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 149. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7881-4_18

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  • DOI: https://doi.org/10.1007/978-3-0348-7881-4_18

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9608-5

  • Online ISBN: 978-3-0348-7881-4

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