Opuscula Math. 41, no. 3 (2021), 283-300
https://doi.org/10.7494/OpMath.2021.41.3.283
Opuscula Mathematica
New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry
Daniel Alpay
Palle E.T. Jorgensen
Abstract. 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.
Keywords: reproducing kernel, positive definite functions, approximation, algorithms, measures, stochastic processes.
Mathematics Subject Classification: 46E22, 43A35.
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- Daniel Alpay (corresponding author)
https://orcid.org/0000-0002-7612-3598- Schmid College of Science and Technology, Chapman University, One University Drive Orange, California 92866, USA
- Palle E.T. Jorgensen
- https://orcid.org/0000-0003-2681-5753
- The University of Iowa, Department of Mathematics, 14C McLean Hall, Iowa City, IA 52246, USA
- Communicated by Aurelian Gheondea.
- Received: 2020-11-20.
- Accepted: 2021-01-23.
- Published online: 2021-04-19.
