Premium
Commutativity of the Valdivia–Vogt table of representations of function spaces
Author(s) -
Bargetz Christian
Publication year - 2014
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.201200258
Subject(s) - mathematics , isomorphism (crystallography) , pure mathematics , sequence (biology) , space (punctuation) , function space , commutative property , interpolation space , table (database) , representation (politics) , algebra over a field , functional analysis , linguistics , chemistry , philosophy , biochemistry , biology , gene , data mining , computer science , crystal structure , politics , law , political science , genetics , crystallography
In this article, we show that the Valdivia–Vogt structure table—containing the sequence space representations of the most used spaces of smooth functions appearing in the theory of distributions—can be interpreted as a commutative diagram, i.e., there is an isomorphism between the space E ( R n ) of infinitely differentiable functions and the spaceC N ⊗ ̂ s , where s is the space of rapidly decreasing sequences, such that its restriction to the other function spaces in the structure table yields an isomorphism between these spaces of smooth functions and their sequence space representation. This result answers the corresponding question of Prof. Dietmar Vogt formulated on the conference “Functional Analysis: Applications to Complex Analysis and Partial Differential Equations” held in Bȩdlewo in May 2012.