A construction of the fundamental solution for Schrödinger equations

Abstract

n this paper, applying the skip method in Fujiwara [3] to the theory of multi-products of Fourier integral operators in Kitada and H.Kumano-go [6], we give a construction of the fundamental solution for the Cauchy problem of a pseudo-differential equation of Schrodinger's type. We regard this construction as a multi-product of Fourier integral operators, and investigate the pointwise convergence of the phase function and that of the symbol. Here we use neither the solution of the Hamilton-Jacobi equation in [6] nor the action of the classical orbit in [2],[4].