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 Mat. Zametki, 1969, Volume 6, Issue 1, Pages 65–72 (Mi mz6898)

M. M. Gekhtman

M. V. Lomonosov Moscow State University

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.

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English version:
Mathematical Notes, 1969, 6:1, 498–502

Bibliographic databases:

UDC: 513.88

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/mz6898} \mathscinet{http://www.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 articles:
1. M. M. Gekhtman, “On the spectrum of an operator Sturm–Liouville equation”, Funct. Anal. Appl., 6:2 (1972), 151–152
2. A. G. Brusentsev, F. S. Rofe-Beketov, “Selfadjointness conditions for strongly elliptic systems of arbitrary order”, Math. USSR-Sb., 24:1 (1974), 103–126
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