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

Opuscula Mathematica

article

Daniel Alpay (corresponding author)¹  Palle E.T. Jorgensen² 

[1] Schmid College of Science and Technology, Chapman University, One University Drive Orange;The University of Iowa, Department of Mathematics

关键词: reproducing kernel;    positive definite functions;    approximation;    algorithms;    measures;    stochastic processes.;   

DOI  :  10.7494/OpMath.2021.41.3.283

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

CC BY-NC