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.

中文翻译：

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关于正定核对拓扑代数的推广

我们定义了从实数或复数设置到拓扑代数的算子值正定函数的扩展，并描述了它们相关的再生核空间。整个函数的情况特别有趣，我们对出现在许多代数中的解析函数的一些幂级数展开给出了精确的含义。