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• Reproducing_kernel_Hilbert_space abstract "In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space associated with a kernel that reproduces every function in the space or, equivalently, where every evaluation functional is bounded. The reproducing kernel was first introduced in the 1907 work of Stanisław Zaremba concerning boundary value problems for harmonic and biharmonic functions. James Mercer simultaneously examined functions which satisfy the reproducing property in the theory of integral equations. The idea of the reproducing kernel remained untouched for nearly twenty years until it appeared in the dissertations of Gábor Szegő, Stefan Bergman, and Salomon Bochner. The subject was eventually systematically developed in the early 1950s by Nachman Aronszajn and Stefan Bergman. These spaces have wide applications, including complex analysis, harmonic analysis, and quantum mechanics. Reproducing kernel Hilbert spaces are particularly important in the field of statistical learning theory because of the celebrated Representer theorem which states that every function in an RKHS can be written as a linear combination of the kernel function evaluated at the training points. This is a practically useful result as it effectively simplifies the empirical risk minimization problem from an infinite dimensional to a finite dimensional optimization problem. For ease of understanding, we provide the framework for real-valued Hilbert spaces. The theory can be easily extended to spaces of complex-valued functions and hence include the many important examples of reproducing kernel Hilbert spaces that are spaces of analytic functions.".
• Reproducing_kernel_Hilbert_space thumbnail Different_Views_on_RKHS.png?width=300.
• Reproducing_kernel_Hilbert_space wikiPageExternalLink 1106.6251,.
• Reproducing_kernel_Hilbert_space wikiPageExternalLink 1110.4017.pdf,.
• Reproducing_kernel_Hilbert_space wikiPageExternalLink rkhs.pdf..
• Reproducing_kernel_Hilbert_space wikiPageExternalLink class03_gdurett.pdf,.
• Reproducing_kernel_Hilbert_space wikiPageExternalLink books.
• Reproducing_kernel_Hilbert_space wikiPageExternalLink kw71.pdf.
• Reproducing_kernel_Hilbert_space wikiPageExternalLink 0002953.pdf,.
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• Reproducing_kernel_Hilbert_space wikiPageRevisionID "682277558".
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Analytic_function.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Analytic_functions.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Bandlimiting.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Bergman_kernel.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Bergman_space.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Borel_measure.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Bounded_operator.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Bulletin_of_the_American_Mathematical_Society.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Category:Hilbert_space.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Cauchy-Schwarz_inequality.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Cauchy–Schwarz_inequality.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Complete_metric_space.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Completion_(metric_space).
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Complex_analysis.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Continuous_function.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Continuous_function_(topology).
• Reproducing_kernel_Hilbert_space wikiPageWikiLink E._H._Moore.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Empirical_risk_minimization.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink File:Different_Views_on_RKHS.png.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Fourier_transform.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Functional_analysis.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Grace_Wahba.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Gábor_Szegő.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink H_square.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Harmonic_analysis.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Hilbert_space.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Holomorphic_function.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Inner_product.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Inner_product_space.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Isomorphic.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Isomorphism.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink James_Mercer_(mathematician).
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Karhunen–Loève_theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Kernel_PCA.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Kernel_embedding_of_distributions.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Kernel_method.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Kernel_principal_component_analysis.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Kernel_trick.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Mathematics.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Mercers_theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Multi-task_learning.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Nachman_Aronszajn.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Plancherel_theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Plancherels_Theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Positive-definite_kernel.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Positive_definite.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Positive_definite_kernel.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Positive_definiteness.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Quantum_mechanics.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Radial_basis_function_kernel.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Real-valued_function.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Representer_theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Riesz_representation_theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Salomon_Bochner.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Set_(mathematics).
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Sinc.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Sinc_function.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Spectral_theorem.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Square-integrable_function.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Stanisław_Zaremba_(mathematician).
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Statistical_learning_theory.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Stefan_Bergman.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Unit_disc.
• Reproducing_kernel_Hilbert_space wikiPageWikiLink Unit_disk.
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "Moore-Aronszajn Theorem".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "Moore–Aronszajn theorem".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "Reproducing Kernel Hilbert Space".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "Reproducing Kernels and Operators with a Cyclic Vector".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "Reproducing kernel Hilbert space".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "linear kernel".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "reproducing kernel Hilbert space".
• Reproducing_kernel_Hilbert_space wikiPageWikiLinkText "reproducing property".
• Reproducing_kernel_Hilbert_space hasPhotoCollection Reproducing_kernel_Hilbert_space.
• Reproducing_kernel_Hilbert_space wikiPageUsesTemplate Template:Cite_journal.
• Reproducing_kernel_Hilbert_space wikiPageUsesTemplate Template:EquationNote.
• Reproducing_kernel_Hilbert_space wikiPageUsesTemplate Template:NumBlk.
• Reproducing_kernel_Hilbert_space wikiPageUsesTemplate Template:Reflist.
• Reproducing_kernel_Hilbert_space subject Category:Hilbert_space.
• Reproducing_kernel_Hilbert_space hypernym Space.
• Reproducing_kernel_Hilbert_space type Mechanic.
• Reproducing_kernel_Hilbert_space type Space.
• Reproducing_kernel_Hilbert_space comment "In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space associated with a kernel that reproduces every function in the space or, equivalently, where every evaluation functional is bounded. The reproducing kernel was first introduced in the 1907 work of Stanisław Zaremba concerning boundary value problems for harmonic and biharmonic functions.".
• Reproducing_kernel_Hilbert_space label "Reproducing kernel Hilbert space".
• Reproducing_kernel_Hilbert_space sameAs Espace_de_Hilbert_à_noyau_reproduisant.
• Reproducing_kernel_Hilbert_space sameAs m.02_nfg.
• Reproducing_kernel_Hilbert_space sameAs Doğuran_çekirdekli_Hilbert_uzayı.

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