CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS

Title & Authors
CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS
KIM KWANG WHOI;

Abstract
We define the convolutions of Fourier hyperfunctions and show that every strongly decreasing Fourier hyperfunction is a convolutor for the space of Fourier hyperfunctions and the converse is true. Also we show that there are no differential operator with constant coefficients which have a fundamental solution in the space of strongly decreasing Fourier hyperfunctions. Lastly we show that the space of multipliers for the space of Fourier hyperfunctions consists of analytic functions extended to any strip in $\small{\mathbb{C}^n}$ which are estimated with a special exponential function exp$\small{(\mu|\chi|)}$.
Keywords
Fourier hyperfunction;convolution;convolution operator;convolutor;pseudodifferential operator;multiplier;
Language
English
Cited by
1.
New spaces of functions and hyperfunctions for Hankel transforms and convolutions, Monatshefte für Mathematik, 2008, 153, 2, 89
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