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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

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Ani Tumanyan (Russian-Armenian (Slavonic) University)

On Index Stability of Differential Operators in Anisotropic Spaces

We study the Fredholm property and index stability of differential linear operators, acting in anisotropic Sobolev spaces in $\mathbb{R}^n$. Conditions are established under which lower order terms of differential operator do not affect the index of the operator. The Fredholm property is studied in anisotropic Sobolev spaces with different weights. We establish sufficient conditions for preservation of the Fredholm property in weighted spaces (see [1]). These results are used in the investigation of the special classes of semielliptical operators. For a semielliptical operator a sufficient condition for the invariance of the index on the scale of anisotropic spaces is obtained in [2]. The influence of numerous applications makes actual the investigation of the index theory of semielliptical operators.

References

[1] Tumanyan A. G. On Noethericity and Index of Differential Operators in Anisotropic Weighted Sobolev Spaces. Proceedings of the Yerevan State University, series Physical and Mathematical sciences, no. 3 (2016), 63-69.
[2] Tumanyan A. G. On the Invariance of Index of Semielliptical Operator on the Scale of Anisotropic Spaces.Journal of Contemporary Mathematical Analysis, vol. 51, no. 4 (2016), 187-198.

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