Lp boundedness, r-nuclearity and approximation of pseudo-differential operators on $\hbar\mathbb{Z}^n$

Abstract

In this work sufficient conditions on the order of the symbol are developed to ensure boundedness, compactness and r-nuclearity of pseudo-differential operators in $\hbar\mathbb{Z}^n$. In addition, these conditions allow us to obtain growth estimates for the eigenvalues of some elliptic operators, in particular perturbed discrete Schr\"odinger operator.