On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball

Abstract

The purpose is to provide a generalization of Carleson's Theorem on interpolating sequences when dealing with a sequence in the open unit ball of a Hilbert space. Precisely, we interpolate a sequence by a function belonging to a weighted Bergman space of infinite order on a unit Hilbert ball and we furnish explicitly the upper bound corresponding to the interpolation constant.

Keywords

• Interpolation sequences
• weighted Bergman spaces
• pseudohyberbolic distance
• Fréchet differentiable functions.
• Analytic functions

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