منابع مشابه
Partitions of Unity and Approximation
We show that for certain translation invariant spaces 5, a necessary and sufficient condition for the eventual denseness of the corresponding scaled spaces Sh is that S contain a stable and locally supported partition of unity. These results have been motivated by recent work on approximation by multivariate piecewise polynomials on regular meshes.
متن کاملConstruction of Scaling Partitions of Unity
Partitions of unity in R formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the functions and matrices yielding such a partition of unity. For expanding matrices, the characterization leads to easy ways of constructing appropriate functions with attracti...
متن کاملPartitions of Unity in Sobolevspaces over Infinite
We prove some general results on the existence of partitions of unity in Sobolev type spaces on various innnite dimensional manifolds. As special cases we obtain in particular, (continuous) partitions of unity a) in the Malliavin test functions on an abstract Wiener space; b) in the rst order Sobolev space on pinned and free loop spaces; c) in the rst order Sobolev spaces associated with revers...
متن کاملSmooth Functions and Partitions of Unity on Certain Banach Spaces
In an earlier paper [4], the author sketched a method, based on the use of “Talagrand operators”, for defining infinitely differentiable equivalent norms on the spaces C0(L) for certain locally compact, scattered spaces L. A special case of this result was that a C renorming exists on C0(L) for every countable locally compact L. Recently, Hájek [3] extended this result by showing that a real no...
متن کاملLinear combinations of partitions of unity with restrictedsupportsChristian
Given a locally nite open covering fC : 2 Ig of a T 4-space X we characterize all real-valued functions f 2 C(X) which admit a representation f = P 2I ' with 2 IR and a partition of unity f' : 2 Ig fulllling the restriction supp(') C. The crucial lemma concerns a particular way of extending partitions of unity in the sense of the Tietze-Urysohn theorem. As an application, we determine the class...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0281155-0