Abstract
Fundamental solutions in a space D′(Mp) of Roumieu ultradistributions are constructed for convolutors f whose Fourier transform\(\hat f\) is slowly decreasing. The solutions are of exponential growth if\(\hat f\) satisfies a stronger condition. These results include a constructive proof of the known existence theorem of Chou. For families of convolutors our method yields solutions which depend continuously on parameters.
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Literatur
CHOU,Ch.Ch.: La transformation de Fourier complexe et l'equation de convolution: Thèse de Doctorat d'Etat, Nice 1969–1970
CIORANESCU, J.: La construction de la solution fondamentale dans les espaces des hyperfonctions: Manuskript, Kiel 1974
GRUDZINSKI,O.v.: Konstruktion von Fundamentallösungen für Convolutoren. manuscripta math.19, 283–317 (1976)
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von Grudzinski, O. Konstruktion von Fundamentallösungen für Convolutoren in roumieuschen Ultradistributionsräumen. Manuscripta Math 20, 263–276 (1977). https://doi.org/10.1007/BF01358641
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DOI: https://doi.org/10.1007/BF01358641