A lifting theorem for formal power series

Bender, Edward A.

doi:10.1090/S0002-9939-1974-0323786-8

A lifting theorem for formal power series
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by Edward A. Bender PDF

Proc. Amer. Math. Soc. 42 (1974), 16-22 Request permission

Abstract:

We define a class of operations on formal power series that includes practically all operations of interest. The class is closed under composition. We prove that an operation in this class vanishes for complex numbers if and only if it vanishes for functions analytic at the origin. A variety of applications of this “lifting theorem” are discussed.

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