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Bögel Functions, Tensor Products and Blending Approximation
Author(s) -
Badea C.,
Cottin C.,
Gonska H. H.
Publication year - 1995
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.19951730103
Subject(s) - mathematics , bounded function , smoothness , pure mathematics , norm (philosophy) , metric space , space (punctuation) , type (biology) , mathematical analysis , function space , combinatorics , linguistics , philosophy , political science , law , biology , ecology
For two compact metric spaces X and Y , we prove that the space of all bounded Bögel functions on X × Y is isometrically isomorphic with the completion of the blending function space M ( X ) ⊗ C ( Y ) + C ( X ) ⊗ M ( Y ) with respect to a suitable norm. This solves a problem raised by G. Freud. Here M ( Z ) and C ( Z ) denote the spaces of all bounded and continuous functions on the metric space Z, respectively. Applications are given to some problems in so‐called blending approximation. All this is based on an abstract Jackson‐type theorem in terms of the entropy numbers of X and Y and the mixed modulus of smoothness.