Communications in Mathematical Physics

, Volume 367, Issue 1, pp 241–263 | Cite as

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

  • M. Burak Erdoğan
  • Michael Goldberg
  • William R. GreenEmail author


In this paper we consider Dirac operators in \({\mathbb{R}^n}\), \({n \ge 2}\), 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 L2 spaces as the frequency goes to infinity.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsUniversity of CincinnatiCincinnatiUSA
  3. 3.Department of MathematicsRose-Hulman Institute of TechnologyTerre HauteUSA

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