Generalized interpolation in the unit ball

Abstract

We study a generalized interpolation problem for the space H[infinity](B2) of bounded homomorphic functions in the ball B2. A sequence Z = {zn} of B2 is an interpolating sequence of order 1 if for all sequence of values wn satisfying conditions of order 1 (that is discrete derivatives in the pseudohyperbolic metric are bounded) there exists a function f [member of] H[infinity](B2) such that f(zn) = wn. These sequences are characterized as unions of 3 free interpolating sequences for H[infinity](B2) such that all triplets of Z made of 3 nearby points have to define an angle uniformly bounded below (in an appropriate sense). Also, we give a multiple interpolation result (interpolation of values and derivatives).