Linear combinations of partitions of unity with restricted supports
Christian Richter
Studia Mathematica, Tome 151 (2002), p. 1-11 / Harvested from The Polish Digital Mathematics Library
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Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation f=∑C∈aCφC with aC∈E and a partition of unity φC:C∈ subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction f|P attains its extrema at vertices of P. Finally, a class of extremal functions on the metric space ([-1,1]m,d∞) is characterized, which appears in approximation by so-called controllable partitions of unity.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:285303 
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     title = {Linear combinations of partitions of unity with restricted supports},
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     year = {2002},
     pages = {1-11},
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Christian Richter. Linear combinations of partitions of unity with restricted supports. Studia Mathematica, Tome 151 (2002) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-1-1/