- 05-145 Takashi Ichinose, Hideo Tamura
- Exponential Product Approximation
to Integral Kernel of Schr\"odinger Semigroup
and to Heat Kernel of Dirichlet Laplacian
Apr 24, 05
(auto. generated ps),
of related papers
Abstract. We know by the studies for the last decade that
the norm convergence of the exponential product formula
holds true even for a class of unbounded operators.
As a natural development of this recent research,
we study how the product formula approximates
integral kernels of Schr\"odinger semigroups.
Our emphasis is placed
on the case of singular potentials.
The Dirichlet Laplacian is regarded
as a special case of Schr\"odinger operators
with singular potentials.
We also discuss the approximation
to the heat kernel generated
by the Dirichlet Laplacian through the product formula.