Geodesic
Fantappi\`e $G$-transform of analytic functionals
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 2, pp. 230-238

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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, Fantappiè transformation, entire functions, continuation of holomorphic functions.
Mots-clés : $G$-transform 
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     author = {Vyacheslav M. Trutnev},
     title = {Fantappi\`e $G$-transform of analytic functionals},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {230--238},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_2_a7/}
}
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Vyacheslav M. Trutnev. Fantappi\`e $G$-transform of analytic functionals. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 2, pp. 230-238. http://geodesic.mathdoc.fr/item/JSFU_2023_16_2_a7/