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Konstruktion von Fundamentallösungen für Convolutoren

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Abstract

We introduce a constructive method for finding fundamental solutions of convolutors in general distribution spaces where a generalized Fourier transform exists and where the topology of the space of test functions can be described by means of an analytic uniform structure in the sense of Ehrenpreis. For convolutors f in a space of Beurling distributions we obtain solutions of unbounded order (resp. of bounded order; resp. of exponential growth) if the Fourier transform of f is slowly (resp. very slowly; resp. extremely slowly) decreasing. These results include constructive proofs of the known existence theorems of Ehrenpreis and Hörmander. For families of convolutors our method yields solutions which depend continuously on parameters.

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  1. Mathematisches Institut der Universität, Olshausenstr. 40-60, D-2300, Kiel 1, Bundesrepublik Deutschland

    Olaf von Grudzinski

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  1. Olaf von Grudzinski
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von Grudzinski, O. Konstruktion von Fundamentallösungen für Convolutoren. Manuscripta Math 19, 283–317 (1976). https://doi.org/10.1007/BF01170777

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  • DOI: https://doi.org/10.1007/BF01170777

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