TY - JOUR

T1 - Limiting Absorption Principle and Strichartz Estimates for Dirac Operators in Two and Higher Dimensions

AU - Burak Erdoğan, M.

AU - Goldberg, Michael

AU - Green, William R.

N1 - Funding Information:
The first author was partially supported by NSF Grant DMS-1501041. The second author is supported by Simons Foundation Grant 281057. The third author is supported by Simons Foundation Grant 511825 and acknowledges the support of a Rose-Hulman summer professional development Grant.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-018-3231-8

DO - 10.1007/s00220-018-3231-8

M3 - Article

AN - SCOPUS:85052646105

SN - 0010-3616

VL - 367

SP - 241

EP - 263

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -