F. Germinet, A. Klein
Operator kernel estimates for functions of
generalized Schrodinger operators
(309K, .ps)
ABSTRACT. We study the decay at large distances of operator kernels of functions
of generalized Schr\"odinger operators, a class of
semibounded second order partial differential
operators of Mathematical Physics, which includes the
Schr\"odinger operator, the magnetic Schr\"odinger operator,
and the classical wave operators (i.e., acoustic operator,
Maxwell operator, and other second order partial differential
operators associated with classical wave equations).
We derive an improved Combes-Thomas estimate, obtaining an explicit lower
bound on the rate of exponential decay of the operator kernel of
the resolvent.
We prove that for slowly
decreasing
smooth functions the operator kernels decay faster
than any polynomial.