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A Fractional Dirac Operator

  • Swanhild BernsteinEmail author
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 252)

Abstract

Based on the Riesz potential, S. Samko and coworkers studied the fractional integro-differentiation of functions of many variables which is a fractional power of the Laplace operator. We will extend this approach to a fractional Dirac operator based on the relation \(D\;=\;\mathcal{H}(-\Delta)^{(-1/2)}\). Because the Hilbert operator \(\mathcal{H}\) is involved as well as the fractional Laplacian of order \({-1/2}\), we will use fractional Hilbert operators and fractional Riesz potentials for the construction.

Keywords

Fractional Dirac operator , fractional Hilbert operator , fractional Laplacian , Riesz potentials , Riesz integro-differentiation , Clifford analysis 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.TU Bergakademie FreibergInstitute of Applied AnalysisFreibergGermany

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