Reproducing kernel Hilbert space: Difference between revisions

Revision as of 17:31, 8 February 2006

Revision as of 18:05, 25 February 2006

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:<math> K(x,y) = K_x(y) </math>

is called a reproducing kernel for the Hilbert space. In fact, ''K'' is uniquely determined by the above condition. In some concrete contexts this amounts to saying

:<math> f(x) = \langle K(x, \cdot), f(\cdot) \rangle </math>

for every ''f''. In some concrete contexts this amounts to saying

:<math>f(x)=\int_\Omega K(x,y) f(y)\,dy</math>