Abstract
We begin with a study of a family of reproducing kernel Hilbert spaces (RKHSs) arising in connection with extension problems for positive definite (p.d.) functions. While the extension problems make sense, and are interesting, in a wider generality, we restrict attention here to the case of continuous p.d. functions defined on open subsets of groups G. We study two questions:
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1.
When is a given partially defined continuous p.d. function extendable to the whole group G? In other words, when does it have continuous p.d. extensions to G?
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2.
When continuous p.d. extensions exist, what is the structure of all continuous p.d. extensions?
It is nice to know that the computer understands the problem. But I would like to understand it too.
— Eugene Wigner
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Jorgensen, P., Pedersen, S., Tian, F. (2016). Extensions of Continuous Positive Definite Functions. In: Extensions of Positive Definite Functions. Lecture Notes in Mathematics, vol 2160. Springer, Cham. https://doi.org/10.1007/978-3-319-39780-1_2
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