An explicit formula for fundamental solutions of linear partial differential equations with constant coefficients

An explicit formula for fundamental solutions of linear partial differential equations with constant coefficients
HTML articles powered by AMS MathViewer

by Heinz König

Proc. Amer. Math. Soc. 120 (1994), 1315-1318

DOI: https://doi.org/10.1090/S0002-9939-1994-1197539-8

PDF | Request permission

References

Leon Ehrenpreis, Solution of some problems of division. I. Division by a polynomial of derivation, Amer. J. Math. 76 (1954), 883–903. MR 68123, DOI 10.2307/2372662
G. B. Folland, Lectures on partial differential equations, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 70, Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1983. MR 696577, DOI 10.1007/978-3-662-00729-7

Linear partial differential operators

Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
Bernard Malgrange, Equations aux dérivées partielles à coefficients constants. I. Solution élémentaire, C. R. Acad. Sci. Paris 237 (1953), 1620–1622 (French). MR 60112

Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution

6

Jean-Pierre Rosay, A very elementary proof of the Malgrange-Ehrenpreis theorem, Amer. Math. Monthly 98 (1991), no. 6, 518–523. MR 1109574, DOI 10.2307/2324871
Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062