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Function cones and interpolation
Author(s) -
Cerdà Joan,
Coll Heribert
Publication year - 2005
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/mana.200310237
Subject(s) - mathematics , interpolation (computer graphics) , cone (formal languages) , function (biology) , bounded function , property (philosophy) , identity (music) , set (abstract data type) , decomposition , pure mathematics , mathematical analysis , algorithm , image (mathematics) , computer science , artificial intelligence , ecology , philosophy , physics , epistemology , evolutionary biology , acoustics , biology , programming language
We consider interpolation of operators acting on functions that belong to a given cone Q with the so‐called decomposition property. The set of all positive functions whose level sets are the level sets of a given function is the main example, and the cone of all decreasing functions is a particular case. As applications, we obtain conditions for the identity ( E 0 ∩ Q,E 1 ∩ Q ) θ,p = ( E 0 , E 1 ) θ,p ∩ Q and interpolation results for operators which are bounded when restricted to a given family of characteristic funcions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)