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A Characterization of White Noise Test Functionals

Published online by Cambridge University Press:  22 January 2016

H.-H. Kuo,
J. Potthoff and
L. Streit
H.-H. Kuo
Affiliation:
Department of Mathematics, Louisiana State University, Batan Rouge, LA 70803, U.S.A.
J. Potthoff
Affiliation:
Department of Mathematics, Louisiana State University, Batan Rouge, LA 70803, U.S.A.
L. Streit
Affiliation:
BiBoS, Universitat Bielefeld, Bielefeld, GermanyArea de Matemätica, Universidade do Minho, Braga, Portugal
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In a recent paper [PS 89], two of the present authors have found a characterization of a certain space (ℐ)* of generalized functionals of white noise, i.e. generalized functionals on ℐ′(R) equipped with the σ-algebra ℬ generated by its cyclinder sets and with the white noise measure μ given by

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 121 , March 1991, pp. 185 - 194
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[Bo 54] Boas, R. P., Entire Functions, New York, Academic Press (1954).Google Scholar
[HKPS] Hida, T., Kuo, H.-H., Potthoff, J. and Streit, L., White Noise: An Infinite Dimensional Calculus, Monograph in preparation.Google Scholar
[HPS 88] Hida, T., Potthoff, J. and Streit, L., Dirichlet forms and white noise analysis, Commun. Math. Phys., 116 (1988), 235–245.Google Scholar
[KT 80] Kubo, I. and Takenaka, S., Calculus on Gaussian white noise I, Proc. Japan Acad., 56A (1980), 376–380.Google Scholar
[PR 89] Potthoff, J. and Roekner, M., On the contraction property of energy forms in infinite dimensions, BiBoS Preprint (1989), to appear in J. Funct. Anal.Google Scholar
[PS 89] Potthoff, J. and Streit, L., A characterization of Hida distributions, BiBoS Preprint, no. 406 (1989).Google Scholar
[Si 71] Simon, B., Distributions and their Hermite expansions; J. Math. Physics, 12 (1971), 140–148.Google Scholar