Generalized interpolation in the unit ball.
We study a generalized interpolation problem for the space H(B) of bounded homomorphic functions in the ball B. A sequence Z = {z} of B is an interpolating sequence of order 1 if for all sequence of values w satisfying conditions of order 1 (that is discrete derivatives in the pseudohyperbolic metric are bounded) there exists a function f ∈ H(B) such that f(z) = w. These sequences are characterized as unions of 3 free interpolating sequences for H(B) such that all triplets of Z made of 3 nearby...