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 (Mercer 1909), is one of the most notable results of the work of James Mercer. 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.
Read more about Mercer's Theorem: Introduction, Details, Trace, Generalizations
Famous quotes containing the words mercer and/or theorem:
“Jeepers creepers!
Where’d ya get those peepers?”
—Johnny Mercer (1909–1976)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)