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. 
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     author = {A. G. Tumanyan},
     title = {On {Noethericity} and index of differential operators in anisotropic weighted {Sobolev} spaces},
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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/