Limiting Absorption Principle and Strichartz Estimates for Dirac Operators in Two and Higher Dimensions

In this paper we consider Dirac operators in R n , n ≥ 2 , with a potential V . Under mild decay and continuity assumptions on V and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent, which implies a family of Strichartz estimates for the linear Di...

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Bibliographic Details
Published in:Communications in mathematical physics 2019-04, Vol.367 (1), p.241-263
Main Authors: Burak Erdoğan, M., Goldberg, Michael, Green, William R.
Format: Article
Language:English
Subjects:
Absorption
Classical and Quantum Gravitation
Complex Systems
Constraining
Decay
Dirac equation
Estimates
Mathematical and Computational Physics
Mathematical Physics
Operators
Physics
Physics and Astronomy
Quantum Physics
Radon
Relativity Theory
Theoretical
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Summary:In this paper we consider Dirac operators in R n , n ≥ 2 , with a potential V . Under mild decay and continuity assumptions on V and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent, which implies a family of Strichartz estimates for the linear Dirac equation. For large potentials the dynamical estimates are not an immediate corollary of the free case since the resolvent of the free Dirac operator does not decay in operator norm on weighted L 2 spaces as the frequency goes to infinity.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3231-8