Some Nonlocal Operators in the First Heisenberg Group

Fractal and Fractional

Ferrari, Fausto¹ 

关键词: Marchaud derivative;    Grünwald–Letnikov derivative;    Heisenberg group;    nonlocal operators;   

DOI  :  10.3390/fractalfract1010015

学科分类：数值分析

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY