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Fractal Fract 2017, 1(1), 15; doi:10.3390/fractalfract1010015

Some Nonlocal Operators in the First Heisenberg Group

Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Received: 1 November 2017 / Revised: 22 November 2017 / Accepted: 23 November 2017 / Published: 27 November 2017
(This article belongs to the Special Issue Fractional Dynamics)
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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. View Full-Text
Keywords: Marchaud derivative; Grünwald–Letnikov derivative; Heisenberg group; nonlocal operators Marchaud derivative; Grünwald–Letnikov derivative; Heisenberg group; nonlocal operators
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ferrari, F. Some Nonlocal Operators in the First Heisenberg Group. Fractal Fract 2017, 1, 15.

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