Geodesic
On Density Conditions for Interpolation in the Ball
Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 559-574

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study interpolating sequences for two related spaces of holomorphic functions in the unit ball of ${{\mathbb{C}}^{n}},\,n\,>\,1$ . We first give density conditions for a sequence to be interpolating for the class ${{A}^{-\infty }}$ of holomorphic functions with polynomial growth. The sufficient condition is formally identical to the characterizing condition in dimension 1, whereas the necessary one goes along the lines of the results given by Li and Taylor for some spaces of entire functions. In the second part of the paper we show that a density condition, which for $n\,=\,1$ coincides with the characterizing condition given by Seip, is sufficient for interpolation in the (weighted) Bergman space.
DOI : 10.4153/CMB-2003-053-x
Mots-clés : 32A36, 32A38, 30E05 
Marco, Nicolas; Massaneda, Xavier. On Density Conditions for Interpolation in the Ball. Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 559-574. doi: 10.4153/CMB-2003-053-x
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