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

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In this paper we consider Dirac operators in $${\mathbb{R}^n}$$Rn, $${n \ge 2}$$n≥2, with a potential V. Under mild decay and continuity assumptions on V and some spectral assumptions on the… Click to show full abstract

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

Keywords: dirac operators; limiting absorption; strichartz estimates; absorption principle

Journal Title: Communications in Mathematical Physics
Year Published: 2017

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