Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Stone–Weierstrass_theorem> ?p ?o. }
Showing items 1 to 30 of
30
with 100 items per page.
- Stone–Weierstrass_theorem abstract "In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation. The original version of this result was established by Karl Weierstrass in 1885 using the Weierstrass transform.Marshall H. Stone considerably generalized the theorem (Stone 1937) and simplified the proof (Stone 1948). His result is known as the Stone–Weierstrass theorem. The Stone–Weierstrass theorem generalizes the Weierstrass approximation theorem in two directions: instead of the real interval [a, b], an arbitrary compact Hausdorff space X is considered, and instead of the algebra of polynomial functions, approximation with elements from more general subalgebras of C(X) is investigated. The Stone–Weierstrass theorem is a vital result in the study of the algebra of continuous functions on a compact Hausdorff space.Further, there is a generalization of the Stone–Weierstrass theorem to noncompact Tychonoff spaces, namely, any continuous function on a Tychonoff space is approximated uniformly on compact sets by algebras of the type appearing in the Stone–Weierstrass theorem and described below.A different generalization of Weierstrass' original theorem is Mergelyan's theorem, which generalizes it to functions defined on certain subsets of the complex plane.".
- Stone–Weierstrass_theorem wikiPageID "28858".
- Stone–Weierstrass_theorem wikiPageRevisionID "600310443".
- Stone–Weierstrass_theorem id "p/s090370".
- Stone–Weierstrass_theorem title "Stone-Weierstrass theorem".
- Stone–Weierstrass_theorem subject Category:Continuous_mappings.
- Stone–Weierstrass_theorem subject Category:Mathematical_analysis.
- Stone–Weierstrass_theorem subject Category:Theorems_in_approximation_theory.
- Stone–Weierstrass_theorem comment "In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation.".
- Stone–Weierstrass_theorem label "Satz von Stone-Weierstraß".
- Stone–Weierstrass_theorem label "Stone–Weierstrass theorem".
- Stone–Weierstrass_theorem label "Teorema de Stone-Weierstrass".
- Stone–Weierstrass_theorem label "Teorema de aproximación de Weierstrass".
- Stone–Weierstrass_theorem label "Teorema di approssimazione di Weierstrass".
- Stone–Weierstrass_theorem label "Théorème de Stone-Weierstrass".
- Stone–Weierstrass_theorem label "Twierdzenie Stone'a-Weierstrassa".
- Stone–Weierstrass_theorem label "Аппроксимационная теорема Вейерштрасса".
- Stone–Weierstrass_theorem label "ストーン＝ワイエルシュトラスの定理".
- Stone–Weierstrass_theorem label "魏尔斯特拉斯逼近定理".
- Stone–Weierstrass_theorem sameAs Stone%E2%80%93Weierstrass_theorem.
- Stone–Weierstrass_theorem sameAs Satz_von_Stone-Weierstraß.
- Stone–Weierstrass_theorem sameAs Teorema_de_aproximación_de_Weierstrass.
- Stone–Weierstrass_theorem sameAs Théorème_de_Stone-Weierstrass.
- Stone–Weierstrass_theorem sameAs Teorema_di_approssimazione_di_Weierstrass.
- Stone–Weierstrass_theorem sameAs ストーン＝ワイエルシュトラスの定理.
- Stone–Weierstrass_theorem sameAs Twierdzenie_Stone'a-Weierstrassa.
- Stone–Weierstrass_theorem sameAs Teorema_de_Stone-Weierstrass.
- Stone–Weierstrass_theorem sameAs Q939927.
- Stone–Weierstrass_theorem sameAs Q939927.
- Stone–Weierstrass_theorem wasDerivedFrom Stone–Weierstrass_theorem?oldid=600310443.