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
  11. E. L. Stout, The second Cousin problem with bounded data, Pacific J. Math 26 (1968), 379-387 Zbl0183.35201MR235155
  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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