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New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry

Alpay Daniel, Jorgensen Palle E.T.

Opuscula Mathematica

2021

Vol. 41, no. 3

283--300

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.

Gelfand-Raikov representations of Coxeter groups associated with positive definite norm functions

Bożejko M., Hirai T.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 1

161--180

The main purpose of the paper is to study the type of Gelfand-Raikov representations of Coxeter groups (W, S) for the special positive definite functions coming from the deformed Poisson (Haagerup) positive definite functions qL(w) for some special length (norm) functions L on Coxeter groups W.