Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 150, Issue 7, Pages 2849-2860Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15661
Keywords
Pseudo-differential operators; minimal and maximal operators; ellipticity; Fredholmness; index
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Funding
- Science and Engineering Research Board (SERB), DST, India [RP03890G]
- Methusalem programme of the Ghent University Special Research Fund (BOF) [01M01021]
- FWO [G.0H94.18N]
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This article proves the coincidence of the minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on Z(n)×T-n, and provides the domain in terms of a Sobolev space. It also demonstrates the equivalence of ellipticity and Fredholmness for pseudo-differential operators on Z(n) and computes the index of an elliptic pseudo-differential operator on Z(n).
The minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on Z(n) x 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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