Fourier Ultra-Hyperfunctions as Boundary Values of Smooth Solutions of the Heat Equation

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Abstract

We consider Fourier ultra-hyperfunctions and characterize them as boundary values of smooth solutions of the heat equation. Namely we show that the convolution of the heat kernel and a Fourier ultra-hyperfunction is a smooth solution of the heat equation with some exponential growth condition and, conversely that such smooth solution can be represented by the convolution of the heat kernel and a Fourier ultra-hyperfunction.

Original languageEnglish
Pages (from-to)381-398
Number of pages18
JournalTokyo Journal of Mathematics
Volume25
Issue number2
DOIs
Publication statusPublished - 2002 Jan 1

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ASJC Scopus subject areas

  • Mathematics(all)

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