On Noethericity and index of differential operators in anisotropic weighted Sobolev spaces

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.