This article is cited in 3 scientific papers (total in 3 papers)
On some topological and geometrical properties of Frechet–Hilbert spaces
D. N. Zarnadze
Muskhelishvili Institute of Computational Mathematics
This paper contains a thorough investigation of topological, geometrical, and structural properties of Frechet spaces representable as a strict projective limit of a sequence of Hilbert spaces, and also of their strong duals, which are representable as a strict inductive limit of a sequence of Hilbert spaces. With the help of families of these spaces, representations are given for the topologies of strict inductive limits of nuclear Frechet spaces and their strong duals. In particular, these results are applicable for representing the topologies of the space $\mathscr D$ of test functions and the space $\mathscr D'$ of generalized functions.
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Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:2, 273–288
MSC: Primary 46A13, 46C05; Secondary 46B20
D. N. Zarnadze, “On some topological and geometrical properties of Frechet–Hilbert spaces”, Izv. RAN. Ser. Mat., 56:5 (1992), 1001–1020; Russian Acad. Sci. Izv. Math., 41:2 (1993), 273–288
Citation in format AMSBIB
\paper On some topological and geometrical properties of Frechet--Hilbert spaces
\jour Izv. RAN. Ser. Mat.
\jour Russian Acad. Sci. Izv. Math.
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D. N. Zarnadze, “A generalization of the method of least squares for operator equations in some Frechet spaces”, Izv. Math., 59:5 (1995), 935–948
R Michael Howe, J Phys A Math Gen, 30:8 (1997), 2757
Freyn W.D., “Tame Fréchet submanifolds of co-Banach type”, Forum Math., 27:4 (2015), 2467–2490
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