A REPRESENTATION OF THE DELTA-FUNCTION VIA CREATION OPERATORS AND GAUSSIAN EXPONENTIALS, AND MULTIPLICATIVE FUNDAMENTAL SOLUTION ASYMPTOTICS FOR SOME PARABOLIC PSEUDODIFFERENTIAL-EQUATIONS

The Dirac delta function is represented as the Gaussian exponential ac ted on by a Gaussian function of the creation operator. On the basis o f this representation, multiplicative asymptotics of fundamental solut ions to certain operators with pure imaginary characteristics are deri ved from the asymptotic representations of the solutions to the corres ponding Cauchy problems with Gaussian initial data.