  It is well-known that the asymptotic expansion of the trace of the heat
kernel for Laplace operators on smooth compact Riemmanian manifolds can be
obtained through termwise integration of the asymptotic expansion of the
on-diagonal heat kernel. It is the purpose of this work to show that, in
certain circumstances, termwise integration can be used to obtain the
asymptotic expansion of the heat kernel trace for Laplace operators endowed
with a suitable polynomial potential on unbounded domains. This is achieved by
utilizing a resummed form of the asymptotic expansion of the on-diagonal heat
kernel.
