We study a generalized interpolation problem for the space H∞(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 ∈ H∞(B2) such that f(zn) = wn. These sequences are characterized as unions of 3 free interpolating sequences for H∞(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).
@article{urn:eudml:doc:41421,
title = {Generalized interpolation in the unit ball.},
journal = {Publicacions Matem\`atiques},
volume = {45},
year = {2001},
pages = {235-257},
mrnumber = {MR1829587},
zbl = {0988.30026},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41421}
}
Marco, Nicolas. Generalized interpolation in the unit ball.. Publicacions Matemàtiques, Tome 45 (2001) pp. 235-257. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41421/