Quasi-isometric vector bundles and bounded factorization of holomorphic matrices

Bo Berndtsson[1]; Jean-Pierre Rosay[2]

  • [1] Chalmers University of Technology and the University of Göteborg, Department of Mathematics, 412 96 Göteborg (Suède)
  • [2] University of Wisconsin, Department of Mathematics, Madison WI 53706 (USA)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 3, page 885-901
  • ISSN: 0373-0956

Abstract

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We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.

How to cite

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Berndtsson, Bo, and Rosay, Jean-Pierre. "Quasi-isometric vector bundles and bounded factorization of holomorphic matrices." Annales de l’institut Fourier 53.3 (2003): 885-901. <http://eudml.org/doc/116057>.

@article{Berndtsson2003,
abstract = {We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.},
affiliation = {Chalmers University of Technology and the University of Göteborg, Department of Mathematics, 412 96 Göteborg (Suède); University of Wisconsin, Department of Mathematics, Madison WI 53706 (USA)},
author = {Berndtsson, Bo, Rosay, Jean-Pierre},
journal = {Annales de l’institut Fourier},
keywords = {vector bundle; maximum principle; holomorphic vector bundle; Hermitian vector bundle; Hermitian holomorphic vector bundle},
language = {eng},
number = {3},
pages = {885-901},
publisher = {Association des Annales de l'Institut Fourier},
title = {Quasi-isometric vector bundles and bounded factorization of holomorphic matrices},
url = {http://eudml.org/doc/116057},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Berndtsson, Bo
AU - Rosay, Jean-Pierre
TI - Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 3
SP - 885
EP - 901
AB - We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.
LA - eng
KW - vector bundle; maximum principle; holomorphic vector bundle; Hermitian vector bundle; Hermitian holomorphic vector bundle
UR - http://eudml.org/doc/116057
ER -

References

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  9. N. Nikolskii, Treatise on the shift operator. Spectral function theory, 273 (1986), Springer-Verlag, Berlin Zbl0587.47036MR827223
  10. G. Segal, A. Pressley, Loop groups, (1986), Oxford Science Publications. The Clarendon Press, Oxford Univer, New York Zbl0618.22011MR900587
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  12. E.L. Stout, On the multiplicative Cousin problem with bounded data, Ann. Scuola Norm. Sup. Pisa 27 (1973), 1-17 Zbl0261.32008MR367282
  13. N. Wiener, P. Masani, The prediction theory of multivariate stochastic processes I. The regularity condition, Acta Math. 98 (1957) Zbl0080.13002MR97856

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