05-145 Takashi Ichinose, Hideo Tamura

Exponential Product Approximation to Integral Kernel of Schr\"odinger Semigroup and to Heat Kernel of Dirichlet Laplacian (543K, ps.file) Apr 24, 05

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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.

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