Ellipticity and Fredholmness of pseudo-differential operators on $\ell^2(\Zn)$

Aparajita Dasgupta; Vishvesh Kumar

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arXiv · 1910.05582

Ellipticity and Fredholmness of pseudo-differential operators on $\ell^2(\Zn)$

Aparajita Dasgupta·Vishvesh Kumar

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Abstract

The minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on $\Z^n\times \mathbb{T}^n$ are proved to coincide and the domain is given in terms of a Sobolev space. Ellipticity and Fredholmness are proved to be equivalent for pseudo-differential operators on $\Z^n$. The index of an elliptic pseudo-differential operator on $\Z^n$ is also computed.

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Aparajita Dasgupta, Vishvesh Kumar. 2019-10-12. Ellipticity and Fredholmness of pseudo-differential operators on $\ell^2(\Zn)$. https://arxiv.org/abs/1910.05582

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