no. 3
Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
Berndtsson, Bo1; Rosay, Jean-Pierre2
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, Volume 53 (2003) no. 3, pp. 885-901.

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.

Nous donnons une condition suffisante pour qu'un fibré vectoriel holomorphe hermitien sur le disque soit quasi isométrique au fibré trivial. Une des conséquences est une version du Lemme de Cartan sur la factorisation des matrices holomorphes pour les matrices holomorphes bornées.

DOI: 10.5802/aif.1964
Classification: 46F20, 32A26
Keywords: vector bundle, maximum principle
Berndtsson, Bo 1; Rosay, Jean-Pierre 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) 
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Berndtsson, Bo; Rosay, Jean-Pierre. Quasi-isometric vector bundles and bounded factorization of holomorphic matrices. Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 885-901. doi : 10.5802/aif.1964. https://aif.centre-mersenne.org/articles/10.5802/aif.1964/

[1] L. Alexandersson On vanishing-curvature extensions of Lorentzian metrics, J. Geom. Anal, Volume 4 (1994) no. 4 | MR | Zbl

[2] B. Berndtsson ∂ ¯ b and Carleson type inequalities, Complex analysis, II (College Park, Md., 1985--86) (Lecture Notes in Math), Volume 1276 (1987), pp. 42-54 | Zbl

[3] A. Beurling On two problems concerning linear transformations in Hilbert space, Acta Math, Volume 81 (1948) | MR | Zbl

[4] A. Brudnyi Matrix-valued Corona theorem for multiply connected domains, Indiana Univ. Math. J, Volume 49 (2000) no. 4 | MR | Zbl

[5] G. D. Birkhoff A theorem on matrices of analytic functions, Math. Ann, Volume 74 (1913) | MR

[6] S. K. Donaldson; P. B. Kronheimer The geometry of four-manifolds, Oxford Mathematical Monographs, Oxford Science Publications. The Clarendon Press, Oxford Univ, New York, 1990 | MR | Zbl

[7] T. W. Gamelin Wolff's proof of the Corona theorem, Israel J. Math, Volume 37 (1980) no. 1,2, pp. 113-119 | DOI | MR | Zbl

[8] L. Lempert La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France, Volume 109 (1981), pp. 427-474 | Numdam | MR | Zbl

[9] N. Nikolskii Treatise on the shift operator. Spectral function theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 273, Springer-Verlag, Berlin, 1986 | MR | Zbl

[10] G. Segal; A. Pressley Loop groups, Oxford Mathematical Monographs, Oxford Science Publications. The Clarendon Press, Oxford Univer, New York, 1986 | MR | Zbl

[11] E. L. Stout The second Cousin problem with bounded data, Pacific J. Math, Volume 26 (1968), pp. 379-387 | MR | Zbl

[12] E.L. Stout On the multiplicative Cousin problem with bounded data, Ann. Scuola Norm. Sup. Pisa, Volume 27 (1973) no. 3, pp. 1-17 | Numdam | MR | Zbl

[13] N. Wiener; P. Masani The prediction theory of multivariate stochastic processes I. The regularity condition, Acta Math., Volume 98 (1957) | MR | Zbl

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