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.
D. Alpay and I. L. Paiva, "On the extension of positive definite kernels to topological algebras," J. Math. Phys. 61, 063507 (2020); https://doi.org/10.1063/5.0007301
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