JournalsprimsVol. 29 , No. 2DOI 10.2977/prims/1195167274

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

  • Kwang Whoi Kim

    Jeonju University, South Korea
  • Soon-Yeong Chung

    Sogang University, Seoul, South Korea
  • Dohan Kim

    Seoul National University, South Korea
Fourier Hyperfunctions as the Boundary Values of Smooth Solutions of Heat Equations cover

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.