When the kernels were used in themselves, without special or previous consideration of the class to which they belonged, they were called "positive definite.

17 авг. 2005 г. · In this theory a central role is played by the reproducing property of the kernel in respect to the class to which it belongs. The kernel is ...

Let F be a class of functions defined in E, forming a Hilbert space (complex or real). The function K(x, y) of x and y in E is called a reproducing kernel (r.k.).

159,99 $ This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications. In Chapter ...

10 февр. 2003 г. · The simple fact was stressed that a reproducing kernel always possesses prop- erty (1) characteristic of positive hermitian matrices (in the ...

\Bibitem{Aro63} \by N.~Aronszajn \paper Theory of reproducing kernels \jour Matematika \yr 1963 \vol 7 \issue 2 \pages 67--130

In this section, we will show that the general theory of reproducing kernels is fairly fundamental in mathematics by considering linear mappings in the ...

In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional.

Theory of Reproducing Kernels. Author(s): N. Aronszajn. Source: Transactions of the American Mathematical Society, Vol. 68, No. 3 (May, 1950), pp. 337-404.

The theory of reproducing kernels started with two papers of 1921 [449] and. 1922 [45] which dealt with typical reproducing kernels of Szegö and Bergman,.