Fourier Hyperfunctions as the Boundary Values of Smooth Solutions of Heat Equations

Abstract

We show that if a _C_∞-solution u(x, t) of heat equation in R+n+1 does not increase faster than exp[ε(1/t+|x|)] then its boundary value determines a unique Fourier hyperfunction. Also, we prove the decomposition theorem for the Fourier hyper functions. These results generalize the theorems of T. Kawai and T. Matsuzawa for Fourier hyperfunctions and solve a question given by A. Kaneko.