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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Strong nuclearity of dual groups

Banaszczyk W., García N.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 1

75-91

Strongly nuclear spaces were introduced by Martineau and Brudovskij in the sixties. It is known that the dual space of a metrizable nuclear space is not only nuclear, but even strongly nuclear. Nuclear groups were introduced in [4]. They form a class of abelian topological groups which is an analogue of the class of nuclear spaces. It was proved in [4] that the dual group of a metrizable nuclear group is a nuclear group again. In this paper we introduce strongly nuclear groups, an analogue of strongly nuclear spaces, and prove that the dual group of a metrizable nuclear group is strongly nuclear.

Existence of strong solutions to stochastic differential equations in conuclear spaces

Jakubowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

247-252

The existence of an unique strong solutions to stochastic differential equations with respect to a generalized non-homogeneous Wiener process in the dual of a nuclear space is proved under monotonicity condition and conditions which guarantee e~stence of weak solutions.