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Regularity of loop group factorization

Author: Michael Taylor
Journal: Proc. Amer. Math. Soc. 133 (2005), 627-631
MSC (2000): Primary 22E67, 35S05
Published electronically: September 8, 2004
MathSciNet review: 2093088
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. K. Clancey and I. Gohberg, Factorization of Matrix Functions and Singular Integral Operators, Birkhäuser, Boston, 1981. MR 0657762 (84a:47016)
  • 2. A. Pressley and G. Segal, Loop Groups, Oxford Univ. Press, 1986. MR 0900587 (88i:22049)
  • 3. 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

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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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