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On absence of threshold resonances for Schrödinger and Dirac operators

  • * Corresponding author: Fritz Gesztesy

    * Corresponding author: Fritz Gesztesy 
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  • Using a unified approach employing a homogeneous Lippmann-Schwinger-type equation satisfied by resonance functions and basic facts on Riesz potentials, we discuss the absence of threshold resonances for Dirac and Schrödinger operators with sufficiently short-range interactions in general space dimensions.

    More specifically, assuming a sufficient power law decay of potentials, we derive the absence of zero-energy resonances for massless Dirac operators in space dimensions $ n \geqslant 3 $, the absence of resonances at $ \pm m $ for massive Dirac operators (with mass $ m > 0 $) in dimensions $ n \geqslant 5 $, and recall the well-known case of absence of zero-energy resonances for Schrödinger operators in dimension $ n \geqslant 5 $.

    Mathematics Subject Classification: Primary: 35J10, 35Q41, 45P05, 47A11, 47G10; Secondary: 35Q40, 47A10, 81Q10.

    Citation:

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