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Analytic characterizations of infinite dimensional distributions

Centro Vito Volterra, Università di Roma “Tor Vergata”, 00133 Via Columbia 2, Roma, Italy

E-mail Address: accardi@volterra.mat.uniroma2.it

Department of Mathematics, Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea

E-mail Address: uncigji@chungbuk.ac.kr

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, and

Kimiaki Saitô

Department of Mathematics, Meijo University, Nagoya 468, Japan

E-mail Address: ksaito@meijo-u.ac.jp

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https://doi.org/10.1142/S0219025717500072Cited by:2 (Source: Crossref)

Abstract

We revisit the analytic characterization theorem for S-transform of infinite dimensional distributions. Then we prove that the nuclearity of the space of test white noise functionals is a necessary condition for the characterization of the S-transform in terms of analytic and growth conditions.

Communicated by H.-H. Kuo

Keywords:

AMSC: Primary 60H40, Secondary 46F25

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