Abstract
This paper deals with the heat kernel for a two-parameter mixed type operator under a given geodesic connection. Here we present a special initial value condition and an adaptive algebraic method for finding the solution of the associated Hamilton’s system. We construct the action function, volume element, and hence the heat kernel by using the Van Vleck’s formula and by solving the transport equation. Here, the path integral method and the Hamilton–Jacobi equation are also introduced.
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