Mercer's Theorem
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A Mercer's Theorem is a representation theorem which states that any symmetric positive-definite kernel on a compact Hausdorff space can be represented as a sum of a convergent series of product functions.
- See: Kernel Method, Functional Analysis, Definite Bilinear Form, Integral Equation, Hilbert Space, Stochastic Process, Karhunen–Loève Theorem.
References
2023
- (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Mercer's_theorem Retrieved:2023-10-16.
- 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-definite kernel.