• On spectral properties of periodic polyharmonic matrix operators

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      https://www.ias.ac.in/article/fulltext/pmsc/112/01/0117-0130

    • 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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