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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.


This article was originally published in Opuscula Mathematica, volume 41, issue 3, in 2021.

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This work is licensed under a Creative Commons Attribution 4.0 License.



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