Trace formulas for parameter-dependent pseudodifferential operators

TY - JOUR

T1 - Trace formulas for parameter-dependent pseudodifferential operators

AU - Grubb, Gerd

PY - 2002

Y1 - 2002

N2 - Trace expansions for operator families such as the resolvent, the heat operator and the complex powers are established for elliptic problems containing pseudodifferential elements. We consider operators on closed manifolds, as well as operators on compact manifolds with boundary, where suitable boundary conditions must be added. It is found in general that one can obtain expansions, e.g. of the heat operator trace, in powers ta and power-logarithmic terms ta log t, and the stability of the coefficients under perturbations is discussed. A survey is given of the methods relying on pseudodifferential calculus that lead to these results.

AB - Trace expansions for operator families such as the resolvent, the heat operator and the complex powers are established for elliptic problems containing pseudodifferential elements. We consider operators on closed manifolds, as well as operators on compact manifolds with boundary, where suitable boundary conditions must be added. It is found in general that one can obtain expansions, e.g. of the heat operator trace, in powers ta and power-logarithmic terms ta log t, and the stability of the coefficients under perturbations is discussed. A survey is given of the methods relying on pseudodifferential calculus that lead to these results.

M3 - Journal article

SN - 0550-3213

VL - 104

SP - 71

EP - 88

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

ER -