A Hamiltonian Path Integral for a Degenerate Parabolic Pseudo-Differential Operator

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 1, Page 57--72.

Kumano-go, Naoto
A Hamiltonian Path Integral for a Degenerate Parabolic Pseudo-Differential Operator
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Abstract:
The symbol of the fundamental solution for a degenerate parabolic pseudo-differential operator of order $m\,(>0)$ can be described in terms of a Hamiltonian path integral. This Hamiltonian path integral converges in the topology of the symbol class $\Sn$ and in the weak topology of the symbol class $\So$.

Mathematics Subject Classification (1991): Primary 35S10; Secondary 47G05, 58D30
Mathematical Reviews Number: MR1414619

Received: 1994-12-20