Regularity of loop group factorization
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- by Michael Taylor
- Proc. Amer. Math. Soc. 133 (2005), 627-631
- DOI: https://doi.org/10.1090/S0002-9939-04-07667-1
- Published electronically: September 8, 2004
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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.
Bibliographic 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