Reproducing kernel Hilbert space: Difference between revisions

Revision as of 18:16, 12 January 2025

Revision as of 06:51, 29 April 2025

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In this case, ''H'' is isomorphic to <math>\Complex^n</math>.

The case of <math>X= \mathbb{D}</math> (where <math>\mathbb{D}</math> denotes the [[unit disc]]) is more sophisticated. Here the [[Bergman space]] [[HA square|<math>HA^2(\mathbb{D})</math>]] is the space of [[square-integrable function|square-integrable]] [[holomorphic function]]s on <math>\mathbb{D}</math>. It can be shown that the reproducing kernel for <math>HA^2(\mathbb{D})</math> is

:<math>K(x,y)=\frac{1}{\pi}\frac{1}{(1-x\overline{y})^2}.</math>