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 - 0920-5632
VL - 104
SP - 71
EP - 88
JO - Nuclear physics B, Proceedings supplements
JF - Nuclear physics B, Proceedings supplements
ER -