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On Meyer’s equivalence

Published online by Cambridge University Press:  22 January 2016

Jürgen Potthoff
Jürgen Potthoff*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464 Japan, Japan, Department of Mathematics, Technical University Berlin, Strasse d. 17. Juni 135, D-1000, Berlin, 12
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In the recent years there has been a considerable effort to construct and analyze spaces of test and generalized functionals in infinite dimensional situations, cf. [3, 5, 12, 14] and literature quoted there. In particular Meyer [4, 5] has introduced a certain space of “smooth” functionals on the Wiener space, which was used by Watanabe [14] for an elegant formulation of “Malliavin’s calculus” (i.e. he proved a criterion for the existence and regularity of densities of Wiener functionals). This functional space is countably normed and one of its important properties is its algebraic structure. The proof of this property follows from an equivalence of the norms defining the space with a system of norms of Sobolev type [4, 5] (cf. also (1.5), (1.6)).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 111 , September 1988 , pp. 99 - 109
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

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