Miscellaneous Asymptotics

  • Victor Ivrii
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter I apply the results and methods of the previous chapters in order to derive asymptotics of the spectrum for the following problems: in section 12.1 I treat operators in domains with “thick” cusps, in section 12.2 I consider operators with potentials degenerate at infinity (such as the Schrödinger operator with a positively homogeneous potential V 0 ≥ 0 with thick cusp {V 0τ} for any fixed τ > 0); section 12.3 is devoted to maximally hypoelliptic operators with symplectic degeneration variety A. Moreover, section 12.4 is devoted to asymptotics of Riesz means for operators with singularities at separate points and in section 12.5 I treat the same for the Schrödinger operator with strong magnetic field. Finally, in section 12.6 I consider the three-dimensional Schrödinger and Dirac operators with constant magnetic field and with electric potential quickly decreasing at infinity and treat the asymptotics of eigenvalues below the essential spectrum.


Dirac Operator Negative Eigenvalue Principal Part Principal Symbol Final Answer 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Victor Ivrii
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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