Ellipticity and Fredholmness of pseudo-differential operators on ℓ²(ℤⁿ)
- 29 March 2022
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 150 (7), 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 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.Keywords
Funding Information
- Science and Engineering Research Board (RP03890G, Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations, 01M01021)
This publication has 24 references indexed in Scilit:
- $L^p$-nuclear pseudo-differential operators on $\mathbb {Z}$ and $\mathbb {S}^1$Proceedings of the American Mathematical Society, 2013
- Sharp Gårding inequality on compact Lie groupsJournal of Functional Analysis, 2011
- Ellipticity, Fredholmness and spectral invariance of pseudo-differential operators on $${{\mathbb S}^1}$$Journal of Pseudo-Differential Operators and Applications, 2010
- On the Toroidal Quantization of Periodic Pseudo-Differential OperatorsNumerical Functional Analysis and Optimization, 2009
- Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanicsJournal of Physics A: Mathematical and Theoretical, 2009
- Spectral theory of SG pseudo-differential operators on Lp(Rn)Studia Mathematica, 2008
- M ‐elliptic pseudo‐differential operators on Lp(ℝn)Mathematische Nachrichten, 2005
- Pseudodifference Operators on Weighted Spaces, and Applications to Discrete Schrödinger OperatorsActa Applicandae Mathematicae, 2004
- Band-dominated operators with operator-valued coefficients, their Fredholm properties and finite sectionsIntegral Equations and Operator Theory, 2001
- Fredholm pseudo-differential operators on weighted Sobolev spacesArkiv för Matematik, 1983