Abstract
Let P(D) be a polynomial with constant coefficients. We shall construct a fundamental solution of P(D) and study its properties. The existence of fundamental solutions has been established previously by Malgrange (ref. [20] in [D]) and by Ehrenpreis ([B], [C]), but our proof is different and more elementary.
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References
[B] L. Ehrenpreis, Solution of some problems of division I, Amer. J. Math. 76 (1954), 883–903.
[C] L. Ehrenpreis, Solution of some problems II, Amer. J. Math. 77 (1955), 286–292.
[D] L. Hӧrmander, On the theory of general partial differential operators, Acta Math. 94 (1955), 161–248.
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Hörmander, L. (2018). Proof Of The Existence Of Fundamental Solutions And Of Some Inequalities. In: Unpublished Manuscripts . Springer, Cham. https://doi.org/10.1007/978-3-319-69850-2_5
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DOI: https://doi.org/10.1007/978-3-319-69850-2_5
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