Regularized traces and Taylor expansions for the heat semigroup

نویسندگان

  • Michael Hitrik
  • Iosif Polterovich
چکیده

We study heat trace asymptotics for Schrödinger operators using commutator expansions due to Agmon-Kannai and Melin. Closed formulas for coefficients of the scattering phase asymptotics in the short-range case are presented. In the long-range case, following Melin, we consider regularized traces and compute coefficients in their asymptotic expansions. These can be thought of as heat invariants for long-range potentials. We also relate commutator expansions mentioned above to the Taylor expansion for the heat semigroup.

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تاریخ انتشار 2008