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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 5, Pages 1001–1020 (Mi izv916)  

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

Abstract: 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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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:2, 273–288

Bibliographic databases:

UDC: 517.98
MSC: Primary 46A13, 46C05; Secondary 46B20
Received: 22.07.1991

Citation: 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
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\by D.~N.~Zarnadze
\paper On some topological and geometrical properties of Frechet--Hilbert spaces
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 5
\pages 1001--1020
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\zmath{https://zbmath.org/?q=an:0786.46002}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..273Z}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 2
\pages 273--288
\crossref{https://doi.org/10.1070/IM1993v041n02ABEH002261}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993MH85700005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath  isi
    2. R Michael Howe, J Phys A Math Gen, 30:8 (1997), 2757  crossref  mathscinet  zmath  isi
    3. Freyn W.D., “Tame Fréchet submanifolds of co-Banach type”, Forum Math., 27:4 (2015), 2467–2490  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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