Spectral asymptotics for the Schrödinger operator with a non-decaying potential

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  • Mouez Dimassi
    Mouez Dimassi, IMB, (UMR CNRS 7539), Université Bordeaux 1, 33400 Talence, France. E-mail: mdimassi@u-bordeaux.fr
  • Setsuro Fujiié
    Ritsumeikan University, 1-1-1 Noji-Higashi, 525-8577 Kusatsu, Japan. E-mail: fujiie@fc.ritsumei.ac.jp

抄録

<jats:p>We study Schrödinger operators H ( h ) = − h 2 Δ + V ( x ) acting in L 2 ( R n ) for non-decaying potentials V. We give a full asymptotic expansion of the spectral shift function for a pair of such operators in the high energy limit. In particular for asymptotically homogeneous potentials W at infinity of degree zero, we also study the semiclassical asymptotics to give a Weyl formula of the spectral shift function above the threshold max W and Mourre estimates in the range of W except at its critical values.</jats:p>

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