Fantappiè $G$-transform of analytic functionals

Vyacheslav M. Trutnev


Abstract: To each analytic functional on the space $ O'(\mathbb C ^ n) $, a function $ f(z) $ holomorphic in a neighborhood of the origin and an entire function of exponential type $ F(z) $ are associated so that the coefficients $ c_\alpha $ of the power series expansion of $ f(z) $ are given by values of $ F(\alpha) $. We study the problem of finding a connection between the domain where the function $ f(z) $ extends to and the growth of the function $F(z)$.

Keywords: analytic functionals, $G$-transform, Fantappiè transformation, entire functions, continuation of holomorphic functions.

UDC: 517.55

Received: 10.07.2022
Received in revised form: 15.09.2022
Accepted: 20.10.2022

Language: English

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