A Hilbert space approach to bounded analytic extension in the ball Academic Article uri icon

abstract

  • 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 Cn extends to a function in the Schur class of the ball. 1. Introduction. Let Ω be a domain in Cn, n≥ 1, and let V be a complex subvariety of Ω. While the extension of analytic function along V to Ω is a cohomological problem, and was solved by Cartan's Theorem B, the same question for bounded analytic functions is more delicate. Partial solutions to the latter …

publication date

  • March 1, 2003