An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when 0 < p ≤ 1, of Fock-type when 0 < p ≤ 2, and of Bergman-type when 0 < p < ∞. Moreover, if a uniformly discrete sequence has a certain uniform non-uniqueness property with respect to any such Lp space (0 < p < ∞), then it is an interpolation sequence for that space. The proofs of these results are based on an approximation theorem for subharmonic functions, Beurling's results concerning compactwise limits of sequences, and the description of interpolation sequences in terms of Beurling-type densities. Details are carried out only for Fock spaces, which represent the most difficult case.
@article{urn:eudml:doc:41393,
title = {Weak conditions for interpolation in holomorphic spaces.},
journal = {Publicacions Matem\`atiques},
volume = {44},
year = {2000},
pages = {277-293},
mrnumber = {MR1775765},
zbl = {0962.30029},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41393}
}
Schuster, Alexander P; Seip, Kristian. Weak conditions for interpolation in holomorphic spaces.. Publicacions Matemàtiques, Tome 44 (2000) pp. 277-293. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41393/