Interpolating sequences for H1∞(BH)

Abstract

We prove that under the extended Carleson's condition, a sequence (x_n) ⊂ B_H is linear interpolating for H^∞(B_H) for an infinite dimensional Hilbert space H. In particular, we construct the interpolating functions for each sequence and find a bound for the constant of interpolation.

Keywords: Infinite dimensional holomorphy, interpolating sequences, spaces of analytic functions, Hilbert spaces