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Ellipticity and Fredholmness of pseudo-differential operators on ℓ²(ℤⁿ)
Published: 29 March 2022
Proceedings of the American Mathematical Society , Volume 150, pp 2849-2860; https://doi.org/10.1090/proc/15661
Abstract: The minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on
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 . The index of an elliptic pseudo-differential operator on is also computed.
Keywords: Pseudo-differential operators / minimal and maximal operators / ellipticity / Fredholmness / index
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