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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
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
Citation:
M. M. Gekhtman, “Self-adjoint abstract differential operators”, Mat. Zametki, 6:1 (1969), 65–72; Math. Notes, 6:1 (1969), 498–502
Linking options:
https://www.mathnet.ru/eng/mzm6898 https://www.mathnet.ru/eng/mzm/v6/i1/p65
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Abstract page: | 248 | Full-text PDF : | 94 | First page: | 1 |
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