Uniformization Method, Tunnel Canonical Operator, and Asymptotic Solutions of a Degenerate Heat Equation

Abstract The recently developed uniformization method in the theory of semiclassical asymptotics is generalized to the case of parabolic equations and asymptotics given by the tunnel canonical operator. The presentation follows an example of the fundamental solution of the Cauchy problem for a family of degenerate parabolic equations on the half-line.