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A representation of the delta function via creation operators and Gaussian exponentials, and multiplicative fundamental solution asymptotics for some parabolic pseudodifferential equations. (English) Zbl 0945.58024
Summary: The Dirac delta function is represented as the Gaussian exponential acted on by a Gaussian function of the creation operator. On the basis of this representation, multiplicative asymptotics of fundamental solutions to certain operators with pure imaginary characteristics are derived from the asymptotic representations of the solutions to the corresponding Cauchy problems with Gaussian initial data.
MSC:
58J40Pseudodifferential and Fourier integral operators on manifolds
58J35Heat and other parabolic equation methods for PDEs on manifolds
58J37Perturbations; asymptotics (PDE on manifolds)
35S05General theory of pseudodifferential operators
46F10Operations with distributions (generalized functions)
46N20Applications of functional analysis to differential and integral equations