Some Nonlocal Operators in the First Heisenberg Group

Abstract

In this paper we construct some nonlocal operators in the Heisenberg group. Specifically, starting from the Grünwald-Letnikov derivative and Marchaud derivative in the Euclidean setting, we revisit those definitions with respect to the one of the fractional Laplace operator. Then, we define some nonlocal operators in the non-commutative structure of the first Heisenberg group adapting the approach applied in the Euclidean case to the new framework.

Keywords

• Marchaud derivative
• Grünwald–Letnikov derivative
• Heisenberg group
• nonlocal operators