Linear combinations of partitions of unity with restricted supports

• Autorzy: Christian Richter
• Języki publikacji: EN

Abstrakty

EN

Given a locally finite open covering 𝓒 of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation $f = ∑_{C∈𝓒} a_{C}φ_{C}$ with $a_{C} ∈ E$ and a partition of unity ${φ_{C}: C ∈ 𝓒}$ subordinate to 𝓒.
As an application, we determine the class of all functions f ∈ C(|𝒫|) on the underlying space |𝒫| of a Euclidean complex 𝒫 such that, for each polytope P ∈ 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.

Kategorie tematyczne

• 41A30: Approximation by other special function classes
• 49J99: None of the above, but in this section
• 52B11: n -dimensional polytopes
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 153
• Numer: 1
• Strony: 1-11

Daty

wydano

2002

Twórcy

autor

Christian Richter

• Equipe d'Analyse, Université Paris VI, Case 186, 4, Place Jussieu, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/sm153-1-1