About: Generalized Fourier series

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In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions defined on an interval of the real line, which is important, among others, for interpolation theory.

Attributes	Values
rdfs:label	Generalized Fourier series (en) Série de Fourier généralisée (fr)
rdfs:comment	In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions defined on an interval of the real line, which is important, among others, for interpolation theory. (en) En analyse, plusieurs extensions du concept de série de Fourier se sont montrées utiles. Elles permettent ainsi d'écrire des décompositions de fonctions sur une base hilbertienne liée à un produit scalaire particulier.Le cas considéré est celui de fonctions de carré intégrable sur un intervalle de la droite réelle, ce qui a des applications, par exemple, en théorie de l'interpolation. (fr)
dcterms:subject	Fourier analysis
Wikipage page ID	245530 (xsd:integer)
Wikipage revision ID	1088752161 (xsd:integer)
Link from a Wikipage to another Wikipage	Fourier analysis Almost everywhere Bessel's inequality Vector space Interpolation Mathematical analysis Orthogonal Orthogonal basis Orthogonality Legendre polynomials Sturm–Liouville theory Function space Orthonormal basis Banach space Topological vector space Least-squares spectral analysis Fourier series Fractional Fourier transform Parseval's theorem Complex conjugation Hilbert space Interval (mathematics) L2 space Weight function Square-integrable Inner product Inner product space Real line Orthogonal function Eigenfunctions
sameAs	Generalized Fourier series Generalized Fourier series Generalized Fourier series Generalized Fourier series Generalized Fourier series
dbp:wikiPageUsesTemplate	dbt:Short_description dbt:Unreferenced dbt:Use_American_English
has abstract	In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions defined on an interval of the real line, which is important, among others, for interpolation theory. (en) En analyse, plusieurs extensions du concept de série de Fourier se sont montrées utiles. Elles permettent ainsi d'écrire des décompositions de fonctions sur une base hilbertienne liée à un produit scalaire particulier.Le cas considéré est celui de fonctions de carré intégrable sur un intervalle de la droite réelle, ce qui a des applications, par exemple, en théorie de l'interpolation. (fr)
prov:wasDerivedFrom	wikipedia-en:Generalized_Fourier_series?oldid=1088752161&ns=0
page length (characters) of wiki page	4063 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Generalized_Fourier_series
is Link from a Wikipage to another Wikipage of	Approximation theory Representation theory of the Lorentz group DFT matrix Vladimir Steklov (mathematician) List of harmonic analysis topics Orthogonal functions Hough function Orthonormal basis Schauder basis Least-squares function approximation Fourier analysis Non-uniform discrete Fourier transform Fourier Fourier–Bessel series List of Fourier analysis topics List of Russian mathematicians List of Russian scientists Helmholtz equation Spiru Haret Classical orthogonal polynomials Orthogonal polynomials Generalized fourier series List of things named after Adrien-Marie Legendre List of things named after Joseph Fourier List of Russian people
is Wikipage redirect of	Generalized fourier series
is Wikipage disambiguates of	Fourier
is foaf:primaryTopic of	wikipedia-en:Generalized_Fourier_series

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