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We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Mathematical Physics, volume 61, in 2020 following peer review. The definitive publisher-authenticated version of this article appeared in

D. Alpay and I. L. Paiva, "On the extension of positive definite kernels to topological algebras," J. Math. Phys. 61, 063507 (2020);

and may be found at xxxx.

Peer Reviewed



Copyright (2020) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.



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