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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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