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This article is cited in 4 scientific papers (total in 4 papers)
Smooth approximation of selfadjoint differential operators of divergence form with bounded measurable coefficients
Yu. B. Orochko
Abstract:
Suppose that $S=-\sum_{j,k=1}^m\frac\partial{\partial x_j}a_{jk}(x)\frac\partial{\partial x_k}+1$ is a uniformly elliptic expression in $\mathbf R^m$, $m\geqslant1$, with real
measurable coefficients, and $A$ is the selfadjoint operator associated with the sesquilinear form $a[f,g]$ in $L_2(\mathbf R^m)$ constructed from $S$; $a[f,g]$ is the limit of a sequence $a_n[f,g]$ ($n=1,2,\dots$) of analogous forms constructed from expressions of the type $S$, but with smooth coefficients. For forms in abstract Hilbert space we prove theorems that imply
the strong convergence of $\Phi(A_n)$ ($A_n$ is the operator associated with $a_n$, and $\Phi(\lambda)$ is a bounded continuous function on the half-line $\lambda\geqslant0$) to $\Phi(A)$ as $n\to\infty$. Applications to the spectral theory of the operator $A$ are given.
Bibliography: 14 titles.
Received: 22.12.1977
Citation:
Yu. B. Orochko, “Smooth approximation of selfadjoint differential operators of divergence form with bounded measurable coefficients”, Mat. Sb. (N.S.), 109(151):3(7) (1979), 418–431; Math. USSR-Sb., 37:3 (1980), 389–401
Linking options:
https://www.mathnet.ru/eng/sm2368https://doi.org/10.1070/SM1980v037n03ABEH001964 https://www.mathnet.ru/eng/sm/v151/i3/p418
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Abstract page: | 377 | Russian version PDF: | 90 | English version PDF: | 12 | References: | 46 |
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