Spectral asymptotics in the semi-classical limit [E-Book] / Mouez Dimassi, Johannes Sjöstrand.
Dimassi, Mouez, (author)
Sjöstrand, J., (author)
Cambridge : Cambridge University Press, 1999
1 online resource (xi, 227 pages)
London Mathematical Society lecture note series ; 268
Full Text
Table of Contents:
  • Local symplectic geometry
  • The WKB-method
  • The WKB-method for a potential minimum
  • Self-adjoint operators
  • The method of stationary phase
  • Tunnel effect and interaction matrix
  • @h-pseudodifferential operators
  • Functional calculus for pseudodifferential operators
  • Trace class operators and applications of the functional calculus
  • More precise spectral asymptotics for non-critical Hamiltonians
  • Improvement when the periodic trajectories form a set of measure 0
  • A more general study of the trace
  • Spectral theory for perturbed periodic problems
  • Normal forms for some scalar pseudodifferential operators
  • Spectrum of operators with periodic bicharacteristics.