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


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Article Info

DATE

2019-04

AUTHORS

M. Burak Erdoğan, Michael Goldberg, William R. Green

ABSTRACT

In this paper we consider Dirac operators in Rn, 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. More... »

PAGES

241-263

References to SciGraph publications

  • 2016-04. The Cubic Dirac Equation: Small Initial Data in H12(R2) in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-11. Limiting Absorption Principle for Some Long Range Perturbations of Dirac Systems at Threshold Energies in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-12. Stable Directions for Small Nonlinear Dirac Standing Waves in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2009-06. Magnetic virial identities, weak dispersion and Strichartz inequalities in MATHEMATISCHE ANNALEN
  • 2004-03. Time decay for solutions of Schrödinger equations with rough and time-dependent potentials in INVENTIONES MATHEMATICAE
  • 1970-03. On the spectrum of the Dirac operator in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2015-01. Effective Limiting Absorption Principles, and Applications in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2017-06. The Dirac Equation in Two Dimensions: Dispersive Estimates and Classification of Threshold Obstructions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2018-07. On the Global Limiting Absorption Principle for Massless Dirac Operators in ANNALES HENRI POINCARÉ
  • 2015-04. The Cubic Dirac Equation: Small Initial Data in H1(R3) in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00220-018-3231-8

    DOI

    http://dx.doi.org/10.1007/s00220-018-3231-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1106272641


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