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Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
-
Takashi Ichinose
and
Hideo Tamura
Published/Copyright:
May 4, 2006
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 Schrödinger semigroups. Our emphasis is placed on the case of singular potentials. The Dirichlet Laplacian is regarded as a special case of Schrödinger operators with singular potentials. We also discuss the approximation to the heat kernel generated by the Dirichlet Laplacian through the product formula.
Received: 2004-09-08
Revised: 2005-04-11
Published Online: 2006-05-04
Published in Print: 2006-03-24
© Walter de Gruyter
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Articles in the same Issue
- Lines on projective hypersurfaces
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- On the growth rate of the tunnel number of knots
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- Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
- κ-types and Γ-asymptotic expansions
