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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Regularity of loop group factorization
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by Michael Taylor PDF
Proc. Amer. Math. Soc. 133 (2005), 627-631 Request permission

Abstract:

In the factorization of a $\operatorname {Gl}(n,\mathbb {C})$-valued loop $\varphi$ into a unitary factor and a factor holomorphic in the disk, it is shown that the two factors each have as much regularity as $\varphi$, measured in a variety of function spaces, though with exceptions. This is analogous to known results for Birkhoff factorization, but somewhat different techniques are involved.
References
  • Kevin F. Clancey and Israel Gohberg, Factorization of matrix functions and singular integral operators, Operator Theory: Advances and Applications, vol. 3, Birkhäuser Verlag, Basel-Boston, Mass., 1981. MR 657762, DOI 10.1007/978-3-0348-5492-4
  • Andrew Pressley and Graeme Segal, Loop groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1986. Oxford Science Publications. MR 900587
  • M. Taylor, Commutator estimates for Hölder continuous multipliers and variants, Preprint, 2003.
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Additional Information
  • Michael Taylor
  • Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
  • MR Author ID: 210423
  • Email: met@math.unc.edu
  • Received by editor(s): October 23, 2003
  • Published electronically: September 8, 2004
  • Additional Notes: This work was partially supported by the National Science Foundation
  • Communicated by: Andreas Seeger
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 627-631
  • MSC (2000): Primary 22E67, 35S05
  • DOI: https://doi.org/10.1090/S0002-9939-04-07667-1
  • MathSciNet review: 2093088