Reproducing kernel Hilbert space: Difference between revisions

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In [[functional analysis]] (a branch of [[mathematics]]), a '''reproducing kernel Hilbert space''' is a [[function space]] in which pointwise evaluation is a [[bounded operator|continuous linear functional]]. Equivalently, they are spaces that can be defined by '''reproducing kernels'''. The subject was originally and simultaneously developed by [[N.Nachman Aronszajn]] and [[Stephan Bergman]] (1895-1987) in [[1950]].

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.