• On spectral properties of periodic polyharmonic matrix operators

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    • Keywords


      Periodic Schrödinger operator; Bloch eigenvalues and eigenfunctions; Bethe-Sommerfeld conjecture

    • Abstract


      We consider a matrix operatorH = (-Δ)l +V inRn, wheren ≥ 2,l ≥ 1, 4l > n + 1, andV is the operator of multiplication by a periodic inx matrixV(x). We study spectral properties ofH in the high energy region. Asymptotic formulae for Bloch eigenvalues and the corresponding spectral projections are constructed. The Bethe-Sommerfeld conjecture, stating that the spectrum ofH can have only a finite number of gaps, is proved.

    • Author Affiliations


      Yu E Karpeshina1

      1. Department of Mathematics, University of Alabama at Birmingham, 452 Campbell Hall, Birmingham, AL - 35294-1170, USA
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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