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)
  • ORCID iD https://orcid.org/0000-0002-7612-3598
  • Schmid College of Science and Technology, Chapman University, One University Drive Orange, California 92866, USA
  • Communicated by Aurelian Gheondea.
  • Received: 2020-11-20.
  • Accepted: 2021-01-23.
  • Published online: 2021-04-19.
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Cite this article as:
Daniel Alpay, Palle E.T. Jorgensen, New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry, Opuscula Math. 41, no. 3 (2021), 283-300, https://doi.org/10.7494/OpMath.2021.41.3.283

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