Roumieu Type Tempered Ultradistributions and Fourier Hyperfunctions
In  we studied spaces of tempered ultradifferential functions and tempered ultradistributions which are globally expressed for the usage of Fourier transforms on R n . These spaces S *, S '* are topologically automorphic to themselves through the Fourier transformation. On the other hand, Kawai and Kaneko have introduced the spaces of Fourier hyperfunctions which are homologically constructed on D n , the compactification of R n to the infinity (cf.  and ). These spaces are also topologically automorphic to themselves through the Fourier transformation.
KeywordsLaplace Transformation Open Cone Common Domain Linear Partial Differential Equation Microlocal Analysis
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