Reproducing kernel Hilbert space: Difference between revisions

Revision as of 23:37, 27 October 2005

Revision as of 23:43, 27 October 2005

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In this article we assume that [[Hilbert space]]s are [[complex number|complex]]. This is because many of the examples of reproducing kernel [[Hilbert space]]s are spaces of analytic functions. Also recall the sesquilinearity convention: the inner product is linear in the second variable.

Let ''X'' be an arbitrary [[set]] and ''H'' a [[Hilbert space]] of complex-valued functions on ''X''. ''H'' is a reproducing kernel Hilbert space if[[iff]] the linear map

:<math> f \mapsto f(x) </math>