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- Wieners_tauberian_theorem abstract "In mathematical analysis, Wiener's tauberian theorem is any of several related results proved by Norbert Wiener in 1932. They provide a necessary and sufficient condition under which any function in L1 or L2 can be approximated by linear combinations of translations of a given function.Informally, if the Fourier transform of a function f vanishes on a certain set Z, the Fourier transform of any linear combination of translations of f also vanishes on Z. Therefore the linear combinations of translations of f can not approximate a function whose Fourier transform does not vanish on Z.Wiener's theorems make this precise, stating that linear combinations of translations of f are dense if and only the zero set of the Fourier transform of f is empty (in the case of L1) or of Lebesgue measure zero (in the case of L2).Gelfand reformulated Wiener's theorem in terms of commutative C*-algebras, when it states that the spectrum of the L1 group ring L1(R) of the group R of real numbers is the dual group of R. A similar result is true when R is replaced by any locally compact abelian group.".
- Wieners_tauberian_theorem wikiPageID "4106793".
- Wieners_tauberian_theorem wikiPageLength "6034".
- Wieners_tauberian_theorem wikiPageOutDegree "17".
- Wieners_tauberian_theorem wikiPageRevisionID "672106119".
- Wieners_tauberian_theorem wikiPageWikiLink Abelian_and_tauberian_theorems.
- Wieners_tauberian_theorem wikiPageWikiLink C*-algebra.
- Wieners_tauberian_theorem wikiPageWikiLink Category:Harmonic_analysis.
- Wieners_tauberian_theorem wikiPageWikiLink Category:Real_analysis.
- Wieners_tauberian_theorem wikiPageWikiLink Category:Tauberian_theorems.
- Wieners_tauberian_theorem wikiPageWikiLink Commutative_C*-algebra.
- Wieners_tauberian_theorem wikiPageWikiLink Dense_set.
- Wieners_tauberian_theorem wikiPageWikiLink Fourier_transform.
- Wieners_tauberian_theorem wikiPageWikiLink Lebesgue_measure.
- Wieners_tauberian_theorem wikiPageWikiLink Linear_combination.
- Wieners_tauberian_theorem wikiPageWikiLink Linear_span.
- Wieners_tauberian_theorem wikiPageWikiLink Locally_compact_abelian_group.
- Wieners_tauberian_theorem wikiPageWikiLink Lp_space.
- Wieners_tauberian_theorem wikiPageWikiLink Mathematical_analysis.
- Wieners_tauberian_theorem wikiPageWikiLink Norbert_Wiener.
- Wieners_tauberian_theorem wikiPageWikiLink Pontryagin_duality.
- Wieners_tauberian_theorem wikiPageWikiLink Shift_operator.
- Wieners_tauberian_theorem wikiPageWikiLink Tauberian_theorem.
- Wieners_tauberian_theorem wikiPageWikiLink Wiener_algebra.
- Wieners_tauberian_theorem wikiPageWikiLink Zero_set.
- Wieners_tauberian_theorem wikiPageWikiLinkText "Wiener's tauberian theorem".
- Wieners_tauberian_theorem authorLink "Israel Gelfand".
- Wieners_tauberian_theorem first "A.I.".
- Wieners_tauberian_theorem hasPhotoCollection Wieners_tauberian_theorem.
- Wieners_tauberian_theorem id "W/w097950".
- Wieners_tauberian_theorem last "Gelfand".
- Wieners_tauberian_theorem last "Shtern".
- Wieners_tauberian_theorem title "Wiener Tauberian theorem".
- Wieners_tauberian_theorem wikiPageUsesTemplate Template:Citation.
- Wieners_tauberian_theorem wikiPageUsesTemplate Template:Eom.
- Wieners_tauberian_theorem wikiPageUsesTemplate Template:Harvs.
- Wieners_tauberian_theorem wikiPageUsesTemplate Template:Math.
- Wieners_tauberian_theorem wikiPageUsesTemplate Template:Reflist.
- Wieners_tauberian_theorem year "1941".
- Wieners_tauberian_theorem subject Category:Harmonic_analysis.
- Wieners_tauberian_theorem subject Category:Real_analysis.
- Wieners_tauberian_theorem subject Category:Tauberian_theorems.
- Wieners_tauberian_theorem comment "In mathematical analysis, Wiener's tauberian theorem is any of several related results proved by Norbert Wiener in 1932. They provide a necessary and sufficient condition under which any function in L1 or L2 can be approximated by linear combinations of translations of a given function.Informally, if the Fourier transform of a function f vanishes on a certain set Z, the Fourier transform of any linear combination of translations of f also vanishes on Z.".
- Wieners_tauberian_theorem label "Wiener's tauberian theorem".
- Wieners_tauberian_theorem sameAs Théorème_taubérien_de_Wiener.
- Wieners_tauberian_theorem sameAs m.0bjfxd.
- Wieners_tauberian_theorem sameAs Общая_тауберова_теорема_Винера.
- Wieners_tauberian_theorem sameAs Q3527279.
- Wieners_tauberian_theorem sameAs Q3527279.
- Wieners_tauberian_theorem wasDerivedFrom Wieners_tauberian_theoremoldid=672106119.
- Wieners_tauberian_theorem isPrimaryTopicOf Wieners_tauberian_theorem.