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 D of test functions and the space D′ of generalized functions.
Citation:
D. N. Zarnadze, “On some topological and geometrical properties of Frechet–Hilbert spaces”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 273–288
\Bibitem{Zar92}
\by D.~N.~Zarnadze
\paper On some topological and geometrical properties of Frechet--Hilbert spaces
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 2
\pages 273--288
\mathnet{http://mi.mathnet.ru/eng/im916}
\crossref{https://doi.org/10.1070/IM1993v041n02ABEH002261}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1209030}
\zmath{https://zbmath.org/?q=an:0786.46002}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..273Z}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993MH85700005}
Linking options:
https://www.mathnet.ru/eng/im916
https://doi.org/10.1070/IM1993v041n02ABEH002261
https://www.mathnet.ru/eng/im/v56/i5/p1001
This publication is cited in the following 5 articles:
Duglas Ugulava, David Zarnadze, “A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators”, Georgian Mathematical Journal, 30:6 (2023), 951
Duglas Ugulava, David Zarnadze, “On linear spline algorithms of computerized tomography in the space of n-orbits”, Georgian Mathematical Journal, 29:6 (2022), 939
Freyn W.D., “Tame Fréchet submanifolds of co-Banach type”, Forum Math., 27:4 (2015), 2467–2490
R Michael Howe, J Phys A Math Gen, 30:8 (1997), 2757
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
Citation in format AMSBIB
Contact us: