A representation of the delta function via creation operators and Gaussian exponentials, and multiplicative fundamental solution asymptotics for some parabolic pseudodifferential equations

Pseudodifferential operators as generalizations of partial differential operators (35S05) Operations with distributions and generalized functions (46F10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37) Applications of functional analysis to differential and integral equations (46N20)

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Nonsmooth nonoscillating WKB-Maslov-type asymptotics for linear parabolic PDE ⋮ Global-in-time asymptotic solutions to Kolmogorov-Feller-type parabolic pseudodifferential equations with small parameter-forward- and backward-in-time motion ⋮ Nonsmooth Nonoscillating Exponential-type Asymptotics for Linear Parabolic PDE ⋮ Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter ⋮ Asymptotics of Fundamental Solutions of Parabolic Problems ⋮ Development of Maslov's approach to the construction of nonoscillating WKB-type solutions ⋮ Forward and backward in time Cauchy problems for systems of parabolic-type PDE with a small parameter

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