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- Wiener's_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.".
- Wiener's_tauberian_theorem wikiPageID "4106793".
- Wiener's_tauberian_theorem wikiPageRevisionID "596787842".
- Wiener's_tauberian_theorem authorLink "Israel Gelfand".
- Wiener's_tauberian_theorem first "A.I.".
- Wiener's_tauberian_theorem hasPhotoCollection Wiener's_tauberian_theorem.
- Wiener's_tauberian_theorem id "W/w097950".
- Wiener's_tauberian_theorem last "Gelfand".
- Wiener's_tauberian_theorem last "Shtern".
- Wiener's_tauberian_theorem title "Wiener Tauberian theorem".
- Wiener's_tauberian_theorem year "1941".
- Wiener's_tauberian_theorem subject Category:Harmonic_analysis.
- Wiener's_tauberian_theorem subject Category:Real_analysis.
- Wiener's_tauberian_theorem subject Category:Tauberian_theorems.
- Wiener's_tauberian_theorem subject Category:Theorems_in_analysis.
- Wiener's_tauberian_theorem type Abstraction100002137.
- Wiener's_tauberian_theorem type Communication100033020.
- Wiener's_tauberian_theorem type Message106598915.
- Wiener's_tauberian_theorem type Proposition106750804.
- Wiener's_tauberian_theorem type Statement106722453.
- Wiener's_tauberian_theorem type TauberianTheorems.
- Wiener's_tauberian_theorem type Theorem106752293.
- Wiener's_tauberian_theorem type TheoremsInAnalysis.
- Wiener's_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.".
- Wiener's_tauberian_theorem label "Théorème taubérien de Wiener".
- Wiener's_tauberian_theorem label "Wiener's tauberian theorem".
- Wiener's_tauberian_theorem label "Общая тауберова теорема Винера".
- Wiener's_tauberian_theorem sameAs Théorème_taubérien_de_Wiener.
- Wiener's_tauberian_theorem sameAs m.0bjfxd.
- Wiener's_tauberian_theorem sameAs Q3527279.
- Wiener's_tauberian_theorem sameAs Q3527279.
- Wiener's_tauberian_theorem sameAs Wiener's_tauberian_theorem.
- Wiener's_tauberian_theorem wasDerivedFrom Wiener's_tauberian_theorem?oldid=596787842.
- Wiener's_tauberian_theorem isPrimaryTopicOf Wiener's_tauberian_theorem.