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Generalized Interpolation in Bergman Spaces and Extremal Functions
Author(s) -
Hartmann Andreas
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200104)224:1<123::aid-mana123>3.0.co;2-i
Subject(s) - mathematics , interpolation (computer graphics) , hardy space , pure mathematics , zero (linguistics) , bergman kernel , blaschke product , mathematical analysis , computer science , animation , linguistics , philosophy , computer graphics (images)
Abstract In a recent paper A. Schuster and K. Seip [SchS] have characterized interpolating sequences for Bergman spaces in terms of extremal functions (or canonical divisors). As these are natural analogues in Bergman spaces of Blaschke products, this yields a Carleson type condition for interpolation. We intend to generalize this idea to generalized free interpolation in weighted Bergman spaces B p , α as was done by V. Vasyunin [Va1] and N. Nikolski [Ni1] (cf.also [Ha2]) in the case of Hardy spaces. In particular we get a strong necessary condition for free interpolation in B p , α on zero–sets of B p , α –functions that in the special case of finite unions of B p , α –interpolating sequences turns out to be also sufficient.