## Tokyo Journal of Mathematics

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

Masanori SUWA

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 25, Number 2 (2002), 381-398.

Dates
First available in Project Euclid: 5 June 2009

https://projecteuclid.org/euclid.tjm/1244208861

Digital Object Identifier
doi:10.3836/tjm/1244208861

Mathematical Reviews number (MathSciNet)
MR1948672

Zentralblatt MATH identifier
1033.35045

#### Citation

SUWA, Masanori. Fourier Ultra-Hyperfunctions as Boundary Values of Smooth Solutions of the Heat Equation. Tokyo J. Math. 25 (2002), no. 2, 381--398. doi:10.3836/tjm/1244208861. https://projecteuclid.org/euclid.tjm/1244208861

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