Geodesic
On Noethericity and index of differential operators in anisotropic weighted Sobolev spaces
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2016), pp. 63-69

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This paper studies Noethericity and index in anisotropic weighted Sobolev spaces in $\mathbb{R}^m$. Sufficient conditions are established for Noethericity preservation in weighted spaces. Applying the results obtained for operators acting in weighted Sobolev spaces, sufficient condition for semi-elliptic operator to have zero index is found.
Keywords: Noetherian operator, index of operator, weighted Sobolev spaces. 
A. G. Tumanyan. On Noethericity and index of differential operators in anisotropic weighted Sobolev spaces. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2016), pp. 63-69. http://geodesic.mathdoc.fr/item/UZERU_2016_3_a11/
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