Estimates on the modulation spaces for the Dirac equation with potential

In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the perturbed Dirac equation and to obtain the desired estimate...

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Bibliographic Details
Published in:Revista matemática complutense 2019-05, Vol.32 (2), p.305-325
Main Authors: Kato, Keiichi, Naumkin, Ivan
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Dirac equation
Estimates
Geometry
Mathematics
Mathematics and Statistics
Modulation
Quadratic equations
Topology
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Summary:In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the perturbed Dirac equation and to obtain the desired estimates for the solution.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-018-0284-3