About: Mercer's theorem

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In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in, is one of the most notable results of the work of James Mercer (1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also used to characterize a symmetric positive semi-definite kernel.

Attributes	Values
rdfs:label	Mercer's theorem (en)
rdfs:comment	In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in, is one of the most notable results of the work of James Mercer (1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also used to characterize a symmetric positive semi-definite kernel. (en)
sameAs	Mercer's theorem Mercer's theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Harv dbt:Reflist dbt:Springer dbt:Functional_analysis
Subject	Theorems in functional analysis
gold:hypernym	Representation
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Mercer's_theorem?oldid=1060632080&ns=0
Wikipage page ID	303990 (xsd:integer)
page length (characters) of wiki page	10405 (xsd:nonNegativeInteger)
Wikipage revision ID	1060632080 (xsd:integer)
Link from a Wikipage to another Wikipage	Uniform norm Unit sphere Arzelà–Ascoli theorem Borel set Theorems in functional analysis James Mercer (mathematician) David Hilbert Hilbert space Hilbert–Schmidt integral operator Hilbert–Schmidt operator Methoden der mathematischen Physik Positive-definite kernel Definite matrix Definite form Linear map Square-integrable function Compact operator on Hilbert space Compact space Eigenfunction Eigenvalues and eigenvectors Orthonormal basis Orthonormality Spectral theorem Spectral theory Spectral theory of compact operators Equicontinuity First-countable space Fubini's theorem Function (mathematics) Functional analysis Gram matrix Kernel method Symmetric matrix Injective function Integral equation Konrad Jörgens Kosambi–Karhunen–Loève theorem Trace class Absolutely integrable function Stochastic process Theorem Mathematics Real number Representer theorem Richard Courant Sign (mathematics)
has abstract	In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in, is one of the most notable results of the work of James Mercer (1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also used to characterize a symmetric positive semi-definite kernel. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Mercer's_theorem
is Wikipage redirect of	Mercer's condition Mercer condition Semi-definite kernel Mercer Theorem Mercer theorem Mercers theorem
is Link from a Wikipage to another Wikipage of	List of theorems Axis–angle representation Bag-of-words model in computer vision James Mercer (mathematician) Jovan Karamata List of functional analysis topics Compact operator on Hilbert space List of University of Manchester people Empirical orthogonal functions Functional data analysis Gram matrix Kernel method Kernel perceptron Inner product space Kosambi–Karhunen–Loève theorem Isomap Mercer Mercer's condition Mercer condition Mercer Theorem Mercer theorem Mercers theorem
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Mercer's_theorem

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