Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Stone–Weierstrass_theorem> ?p ?o }
- 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 wikiPageExternalLink bibliothek.bbaw.de.
- Stone–Weierstrass_theorem wikiPageExternalLink 1885-2&seite:int=109.
- Stone–Weierstrass_theorem wikiPageExternalLink 1885-2&seite:int=272.
- Stone–Weierstrass_theorem wikiPageID "28858".
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- Stone–Weierstrass_theorem wikiPageWikiLink *-algebra.
- Stone–Weierstrass_theorem wikiPageWikiLink Absolute_value.
- Stone–Weierstrass_theorem wikiPageWikiLink Algebra_over_a_field.
- Stone–Weierstrass_theorem wikiPageWikiLink Associative_algebra.
- Stone–Weierstrass_theorem wikiPageWikiLink Banach_algebra.
- Stone–Weierstrass_theorem wikiPageWikiLink Banach_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Bernstein_polynomial.
- Stone–Weierstrass_theorem wikiPageWikiLink C*-algebra.
- Stone–Weierstrass_theorem wikiPageWikiLink Cardinality.
- Stone–Weierstrass_theorem wikiPageWikiLink Cardinality_of_the_continuum.
- Stone–Weierstrass_theorem wikiPageWikiLink Category:Continuous_mappings.
- Stone–Weierstrass_theorem wikiPageWikiLink Category:Theorems_in_analysis.
- Stone–Weierstrass_theorem wikiPageWikiLink Category:Theorems_in_approximation_theory.
- Stone–Weierstrass_theorem wikiPageWikiLink Closure_(topology).
- Stone–Weierstrass_theorem wikiPageWikiLink Compact-open_topology.
- Stone–Weierstrass_theorem wikiPageWikiLink Compact_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Complex_conjugate.
- Stone–Weierstrass_theorem wikiPageWikiLink Complex_plane.
- Stone–Weierstrass_theorem wikiPageWikiLink Continuous_function.
- Stone–Weierstrass_theorem wikiPageWikiLink Continuous_functions_on_a_compact_Hausdorff_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Countable_set.
- Stone–Weierstrass_theorem wikiPageWikiLink Errett_Bishop.
- Stone–Weierstrass_theorem wikiPageWikiLink Fourier_series.
- Stone–Weierstrass_theorem wikiPageWikiLink German_language.
- Stone–Weierstrass_theorem wikiPageWikiLink Glossary_of_topology.
- Stone–Weierstrass_theorem wikiPageWikiLink Hahn–Banach_theorem.
- Stone–Weierstrass_theorem wikiPageWikiLink Hausdorff_space.
- Stone–Weierstrass_theorem wikiPageWikiLink If_and_only_if.
- Stone–Weierstrass_theorem wikiPageWikiLink Interval_(mathematics).
- Stone–Weierstrass_theorem wikiPageWikiLink Jan_Brinkhuis.
- Stone–Weierstrass_theorem wikiPageWikiLink Karl_Weierstrass.
- Stone–Weierstrass_theorem wikiPageWikiLink Krein–Milman_theorem.
- Stone–Weierstrass_theorem wikiPageWikiLink Lattice_(order).
- Stone–Weierstrass_theorem wikiPageWikiLink Linear_subspace.
- Stone–Weierstrass_theorem wikiPageWikiLink Locally_compact_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Lp_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Marshall_Harvey_Stone.
- Stone–Weierstrass_theorem wikiPageWikiLink Mathematical_analysis.
- Stone–Weierstrass_theorem wikiPageWikiLink Mergelyans_theorem.
- Stone–Weierstrass_theorem wikiPageWikiLink Müntz–Szász_theorem.
- Stone–Weierstrass_theorem wikiPageWikiLink Orthonormal_basis.
- Stone–Weierstrass_theorem wikiPageWikiLink Polynomial.
- Stone–Weierstrass_theorem wikiPageWikiLink Polynomial_interpolation.
- Stone–Weierstrass_theorem wikiPageWikiLink Rational_number.
- Stone–Weierstrass_theorem wikiPageWikiLink Runges_phenomenon.
- Stone–Weierstrass_theorem wikiPageWikiLink Separable_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Separating_set.
- Stone–Weierstrass_theorem wikiPageWikiLink Square-integrable_function.
- Stone–Weierstrass_theorem wikiPageWikiLink Tychonoff_space.
- Stone–Weierstrass_theorem wikiPageWikiLink Uniform_convergence.
- Stone–Weierstrass_theorem wikiPageWikiLink Uniform_norm.
- Stone–Weierstrass_theorem wikiPageWikiLink Vanish_at_infinity.
- Stone–Weierstrass_theorem wikiPageWikiLink Walter_Rudin.
- Stone–Weierstrass_theorem wikiPageWikiLink Weierstrass_transform.
- Stone–Weierstrass_theorem wikiPageWikiLinkText "Stone–Weierstrass theorem".
- Stone–Weierstrass_theorem wikiPageWikiLinkText "Stone–Weierstrass approximation theorem".
- Stone–Weierstrass_theorem wikiPageWikiLinkText "Stone–Weierstrass theorem".
- Stone–Weierstrass_theorem wikiPageWikiLinkText "Stone–Weierstrass theorem#Bishop's theorem".
- Stone–Weierstrass_theorem wikiPageWikiLinkText "Weierstrass approximation theorem".
- Stone–Weierstrass_theorem wikiPageWikiLinkText "Weierstrass theorem".
- Stone–Weierstrass_theorem id "p/s090370".
- Stone–Weierstrass_theorem title "Stone-Weierstrass theorem".
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- Stone–Weierstrass_theorem subject Category:Continuous_mappings.
- Stone–Weierstrass_theorem subject Category:Theorems_in_analysis.
- Stone–Weierstrass_theorem subject Category:Theorems_in_approximation_theory.
- Stone–Weierstrass_theorem type Field.
- Stone–Weierstrass_theorem type Function.
- Stone–Weierstrass_theorem type Mapping.
- Stone–Weierstrass_theorem type Redirect.
- Stone–Weierstrass_theorem type Theorem.
- 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 "Stone–Weierstrass theorem".
- Stone–Weierstrass_theorem sameAs Q939927.
- Stone–Weierstrass_theorem sameAs نظرية_وريشترس.
- 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 משפט_הקירוב_של_ויירשטראס.
- Stone–Weierstrass_theorem sameAs Weierstrass_approximációs_tétele.
- 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 Stelling_van_Stone-Weierstrass.