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June  2003, 2(2): 139-145. doi: 10.3934/cpaa.2003.2.139

A Hilbert space approach to bounded analytic extension in the ball

Daniel Alpay 1, , Mihai Putinar 2, and  Victor Vinnikov 3,

1. 

Department of Mathematics, Ben Gurion University of the Negev, POB 653, Beer Sheva 84105, Israel
2. 

Department of Mathematics, University of California, Santa Barbara CA 93106, United States
3. 

Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel

Received  October 2002 Revised  January 2003 Published  March 2003

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.
Keywords: Schur class., reproducing kernel, Bounded analytic extension.
Mathematics Subject Classification: 32A35, 32A70, 47A4.
Citation: Daniel Alpay, Mihai Putinar, Victor Vinnikov. A Hilbert space approach to bounded analytic extension in the ball. Communications on Pure and Applied Analysis, 2003, 2 (2) : 139-145. doi: 10.3934/cpaa.2003.2.139
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