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- Dirichlet_kernel abstract "In mathematical analysis, the Dirichlet kernel is the collection of functionsIt is named after Peter Gustav Lejeune Dirichlet.The importance of the Dirichlet kernel comes from its relation to Fourier series. The convolution of Dn(x) with any function f of period 2π is the nth-degree Fourier series approximation to f, i.e., we havewhereis the kth Fourier coefficient of f. This implies that in order to study convergence of Fourier series it is enough to study properties of the Dirichlet kernel. Of particular importance is the fact that the L1 norm of Dn diverges to infinity as n → ∞. One can estimate that.This lack of uniform integrability is behind many divergence phenomena for the Fourier series. For example, together with the uniform boundedness principle, it can be used to show that the Fourier series of a continuous function may fail to converge pointwise, in rather dramatic fashion. See convergence of Fourier series for further details.".
- Dirichlet_kernel thumbnail Dirichlet.png?width=300.
- Dirichlet_kernel wikiPageExternalLink books?id=1WY6u0C_jEsC.
- Dirichlet_kernel wikiPageExternalLink DirichletKernel.html.
- Dirichlet_kernel wikiPageID "26611926".
- Dirichlet_kernel wikiPageRevisionID "602932711".
- Dirichlet_kernel hasPhotoCollection Dirichlet_kernel.
- Dirichlet_kernel id "p/d032880".
- Dirichlet_kernel title "Dirichlet kernel".
- Dirichlet_kernel subject Category:Approximation_theory.
- Dirichlet_kernel subject Category:Articles_containing_proofs.
- Dirichlet_kernel subject Category:Fourier_series.
- Dirichlet_kernel subject Category:Mathematical_analysis.
- Dirichlet_kernel comment "In mathematical analysis, the Dirichlet kernel is the collection of functionsIt is named after Peter Gustav Lejeune Dirichlet.The importance of the Dirichlet kernel comes from its relation to Fourier series. The convolution of Dn(x) with any function f of period 2π is the nth-degree Fourier series approximation to f, i.e., we havewhereis the kth Fourier coefficient of f. This implies that in order to study convergence of Fourier series it is enough to study properties of the Dirichlet kernel.".
- Dirichlet_kernel label "Dirichlet kernel".
- Dirichlet_kernel label "Dirichlet-Kern".
- Dirichlet_kernel label "Noyau de Dirichlet".
- Dirichlet_kernel label "Ядро Дирихле".
- Dirichlet_kernel label "ディリクレ核".
- Dirichlet_kernel label "狄利克雷核".
- Dirichlet_kernel sameAs Dirichlet-Kern.
- Dirichlet_kernel sameAs Noyau_de_Dirichlet.
- Dirichlet_kernel sameAs ディリクレ核.
- Dirichlet_kernel sameAs m.019q94.
- Dirichlet_kernel sameAs Q906024.
- Dirichlet_kernel sameAs Q906024.
- Dirichlet_kernel wasDerivedFrom Dirichlet_kernel?oldid=602932711.
- Dirichlet_kernel depiction Dirichlet.png.
- Dirichlet_kernel isPrimaryTopicOf Dirichlet_kernel.