A construction of the fundamental solution for Schrödinger equations
Vol. 2 (1995), No. 2, Page 441--498.
Kumano-go, Naoto
A construction of the fundamental solution for Schrödinger equations
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Abstract:
In 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 Schrödinger'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].
Mathematics Subject Classification (1991): Primary 35S05; Secondary 58D30, 47G30, 58G15
Mathematical Reviews Number: MR1366565
Received: 1994-12-22
