# Generalized interpolation in the unit ball.

• Volume: 45, Issue: 1, page 235-257
• ISSN: 0214-1493

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## Abstract

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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).

## How to cite

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Marco, Nicolas. "Generalized interpolation in the unit ball.." Publicacions Matemàtiques 45.1 (2001): 235-257. <http://eudml.org/doc/41421>.

@article{Marco2001,
abstract = {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).},
author = {Marco, Nicolas},
journal = {Publicacions Matemàtiques},
keywords = {Interpolación; Funciones analíticas; Bola unidad},
language = {eng},
number = {1},
pages = {235-257},
title = {Generalized interpolation in the unit ball.},
url = {http://eudml.org/doc/41421},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Marco, Nicolas
TI - Generalized interpolation in the unit ball.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 1
SP - 235
EP - 257
AB - 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).
LA - eng
KW - Interpolación; Funciones analíticas; Bola unidad
UR - http://eudml.org/doc/41421
ER -

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