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Matematicheskie Zametki, 1969, Volume 6, Issue 1, Pages 65–72 (Mi mzm6898)  

This article is cited in 4 scientific papers (total in 4 papers)

Self-adjoint abstract differential operators

M. M. Gekhtman

M. V. Lomonosov Moscow State University
Full-text PDF (497 kB) Citations (4)
Abstract: Let $H$ be an abstract separable Hilbert space. We will consider the Hilbert space $H_1$ whose elements are functions $f(x)$ with domain $H$ and we will also consider the set of self-adjoint operators $Q(x)$ in $H$ of the form $Q(x)=A+B(x)$. In this formula $A\ge E$, $B(x)\ge0$, and the operator $B(x)$ is bounded for all $x$. An operator $L_0$ is defined on the set of finite, infinitely differentiable (in the strong sense) functions $y(x)\inH_1$ according to the formula: $L_0y=-y''+Q(x)y$ $(-\infty<x<\infty)$. It is proved that the closure of the operator $L_0$ is a self-adjoint operator in $H_1$ under the given assumptions.
Received: 07.02.1968
English version:
Mathematical Notes, 1969, Volume 6, Issue 1, Pages 498–502
DOI: https://doi.org/10.1007/BF01450253
Bibliographic databases:
UDC: 513.88
Language: Russian
Citation: M. M. Gekhtman, “Self-adjoint abstract differential operators”, Mat. Zametki, 6:1 (1969), 65–72; Math. Notes, 6:1 (1969), 498–502
Citation in format AMSBIB
\Bibitem{Gek69}
\by M.~M.~Gekhtman
\paper Self-adjoint abstract differential operators
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 1
\pages 65--72
\mathnet{http://mi.mathnet.ru/mzm6898}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=254667}
\zmath{https://zbmath.org/?q=an:0188.21002|0182.18404}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 1
\pages 498--502
\crossref{https://doi.org/10.1007/BF01450253}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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