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Download e-book for kindle: Complex Analysis, Functional Analysis and Approximation by Jorge Mujica (Eds.)

By Jorge Mujica (Eds.)

This court cases quantity comprises papers of analysis of expository nature, and is addressed to analyze employees and complex graduate scholars in arithmetic. a number of the papers are the written and extended texts of lectures brought on the convention, while others were incorporated via invitation.

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Additional resources for Complex Analysis, Functional Analysis and Approximation Theory, Proceedings of the Conference on Complex Analysis and Approximation Theory Universidade Estadual de Campinas

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And assume F is a Borel set in a B with C a p q ( E ) is a s e t of u n i q u e n e s s for H q if the r e s t r i c t i o n o p e r a t o r RE : ffq E q , which takes any function f € H q Let q E B > 0. We will say that E + to its generalized boundary value on for E, is injective. Our next result characterizes the boundary sets of uniqueness H q . The one dimensional case with q = - 1 is due to Hamilton 43 REPRODUCING KERNELS [12]. (In this case H-l THEOREM 3 . 8 . b e a Bore1 s e t in is the classical space of Dirichlet finite functions in the unit disk).

1 1 p e r s i s t s and C j are allowed t o vary over t h e s e t D. E x E, zi , ,6 when 28 BEATROUS AN0 BURBEA We will present an abstract formulation of this result which admits a particularly simple proof based on Hilbert space considerations, and which yields a significant improvement of the classical result when specialized to the classical setting. For our purposes it will be more convenient to work with a slightly modified version of the Bergman-Schiffer inequality. Let K, and K 2 be positive definite kernels on X, and X 2 respectively.

Given by classical condition that E be a set of uniqueness is not required. In general some such assumption is essential. Korhyi and Pukgnski [141 gave an exampleof a function on a 2 point set in the bi-disk that is not the restricK tion of any function in the unit ball of Hm. For the kernels 1-I introduced above, it is clear that it suffices to assume that E is a set of uniqueness for the holomorphic subspace of L 1 fdul. Moreover, is a multiplier on if for each fixed 5 E D the function K( * , 5 1 HK, then it suffices to assume that E is a set of uniqueness for HK since in this case HK contains the class of functions used in the 36 BEATROUS AND BURBEA theorem.

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