# Weak conditions for interpolation in holomorphic spaces.

Alexander P Schuster; Kristian Seip

Publicacions Matemàtiques (2000)

- Volume: 44, Issue: 1, page 277-293
- ISSN: 0214-1493

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topSchuster, Alexander P, and Seip, Kristian. "Weak conditions for interpolation in holomorphic spaces.." Publicacions Matemàtiques 44.1 (2000): 277-293. <http://eudml.org/doc/41393>.

@article{Schuster2000,

abstract = {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.},

author = {Schuster, Alexander P, Seip, Kristian},

journal = {Publicacions Matemàtiques},

keywords = {Funciones de variable compleja; Conjuntos de interpolación; Funciones holomorfas; subharmonic functions; interpolation sequence; Beurling-type densities; Fock spaces},

language = {eng},

number = {1},

pages = {277-293},

title = {Weak conditions for interpolation in holomorphic spaces.},

url = {http://eudml.org/doc/41393},

volume = {44},

year = {2000},

}

TY - JOUR

AU - Schuster, Alexander P

AU - Seip, Kristian

TI - Weak conditions for interpolation in holomorphic spaces.

JO - Publicacions Matemàtiques

PY - 2000

VL - 44

IS - 1

SP - 277

EP - 293

AB - 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.

LA - eng

KW - Funciones de variable compleja; Conjuntos de interpolación; Funciones holomorfas; subharmonic functions; interpolation sequence; Beurling-type densities; Fock spaces

UR - http://eudml.org/doc/41393

ER -

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