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On normal solvability and Noetherian property for elliptic operators in spaces of functions on \(R^ n\). II. (Russian) Zbl 0577.47045
The author continues his study of semi-Fredholm-properties of elliptic differential operators L with uniformly continuous matrix valued coefficients on \({\mathbb{R}}^ n\) using again the concept of a ”limit operator \(\tilde L\) of L at infinity”. [For part I see ibid. 110, 120-140 (1981; Zbl 0508.47046)].
First the author considers L as an operator from \(S^{\eta,q}\to S^ q\) where \(S^{\eta,q}\) is the completion of \(C_ b^{\eta}({\mathbb{R}}^ n,{\mathbb{R}}^ m)=\{f:{\mathbb{R}}^ n\to {\mathbb{R}}^ m:f\) has continuous bounded derivatives up to the order \(\eta\) \(\}\) in the norm \[ \| u\|_{\eta,q}=\sum_{| \alpha | \leq \eta}\sup_{y\in {\mathbb{R}}^ n}\| D^{\alpha}u\|_{L^ q(K\quad_ y)}, \] where \(K_ y\) is the ball with center y and radius 1, \(S^ q=S^{0,q}\), \(q>1\). Then the author considers L as an operator from \(H^{\eta}\) to \(H^ 0\) where \(H^{\eta}\) is the Sobolev space.
Reviewer: K.-H.Förster

MSC:
47F05 General theory of partial differential operators
47A53 (Semi-) Fredholm operators; index theories
35J30 Higher-order elliptic equations
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