Theorems in functional analysis

Mercer's theorem

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. (Wikipedia).

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Related pages

Functional analysis | Fubini's theorem | Spectral theorem | Kernel method | Stochastic process | Theorem | Richard Courant | David Hilbert | Positive-definite kernel | Representer theorem | James Mercer (mathematician) | Injective function | Square-integrable function | Mathematics | Function (mathematics) | Real number | Orthonormal basis | Symmetric matrix | Trace class | Compact operator on Hilbert space | Eigenfunction | Hilbert space | Integral equation | Uniform norm | Hilbert–Schmidt integral operator | Lp space | Hilbert–Schmidt operator | Spectral theory of compact operators | Unit ball | Spectral theory