Green kernels associated with Riesz kernels

1786 - 0091 Complete Interpolation Vs . Riesz Bases of Reproducing Kernels

In the study of Hilbert spaces of analytic functions, it is noticed that complete interpolating sequences and Riesz bases of reproducing kernels are dual notions. In this work we make this duality explicit by identifying sequences of complex numbers with linear operators.

Reproducing kernels , Bergman kernels , Poisson kernels

String Kernels , Fisher Kernels

In this paper we show how the generation of documents can be thought of as a k-stage Markov process, which leads to a Fisher kernel from which the n-gram and string kernels can be reconstructed. The Fisher kernel view gives a more exible insight into the string kernel and suggests how it can be parametrised in a way that re-ects the statistics of the training corpus. Furthermore, the prob-abili...

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

Kernels, Associated Structures and Generalizations

This paper gives a survey of results in the mathematical literature on positive definite kernels and their associated structures. We concentrate on properties which seem potentially relevant for Machine Learning and try to clarify some results that have been misused in the literature. Moreover we consider different lines of generalizations of positive definite kernels. Namely we deal with opera...