A Hilbert space approach to bounded analytic extension in the ball

Daniel Alpay; Mihai Putinar; Victor Vinnikov

doi:10.3934/cpaa.2003.2.139

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2003, Volume 2, Issue 2: 139-145. Doi: 10.3934/cpaa.2003.2.139

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A Hilbert space approach to bounded analytic extension in the ball

1.
Department of Mathematics, Ben Gurion University of the Negev, POB 653, Beer Sheva 84105
2.
Department of Mathematics, University of California, Santa Barbara CA 93106
3.
Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva 84105

Received: September 30, 2002

Revised: December 31, 2002

Published: May 2003

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Abstract

One proves, using methods of Hilbert spaces with a reproducing kernel, that any bounded analytic function on a complex curve in general position in the unit ball of C$^n$ extends to a function in the Schur class of the ball.

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Mathematics Subject Classification: 32A35, 32A70, 47A48.

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