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A note on quarkonial systems and multilevel partition of unity methods
Author(s) -
Dahlke Stephan,
Oswald Peter,
Raasch Thorsten
Publication year - 2013
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.201100246
Subject(s) - mathematics , partition of unity , partition (number theory) , monomial , connection (principal bundle) , stability (learning theory) , partition function (quantum field theory) , pure mathematics , degree (music) , combinatorics , geometry , computer science , physics , quantum mechanics , finite element method , machine learning , acoustics , thermodynamics
We discuss the connection between the theory of quarkonial decompositions for function spaces developed by Hans Triebel, and the multilevel partition of unity method. The central result is an alternative approach to the stability of quarkonial decompositions in Besov spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$B_{pp}^s({\mathbb {R}}^n)$\end{document} , s > n (1/ p − 1) + , which leads to relaxed decay assumptions on the elements of a quarkonial system as the monomial degree grows.