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Beitrag zum Divisionsproblem für Ultradistributionen und ein Fortsetzungssatz. (German) Zbl 0401.46020


MSC:

46F10 Operations with distributions and generalized functions
35D05 Existence of generalized solutions of PDE (MSC2000)
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References:

[1] BJÖRK, G., Linear partial differential operators and generalized distributions, Ark. Mat.6, S. 351-407 (1966) · Zbl 0166.36501 · doi:10.1007/BF02590963
[2] CHOU, C. C., La Transformation de Fourier Complexe et L’Equation de Convolution, Springer Lecture Notes, Berlin-Heidelberg-New York 1973 · Zbl 0257.46037
[3] DROSTE, B., Divisionsproblem für Ultradistributionen, Diplomarbeit, Kaiserslautern 1976 · Zbl 0401.46020
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[5] GROTHENDIECK, A., Topological Vector Spaces, Gordon and Breach, 1973 · Zbl 0275.46001
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[8] KOMATSU, H., Ultradistributions, I Structure theorems and a characterization, J. Fac. Sc. Univ. Tokyo20, S. 25-105, (1973) · Zbl 0258.46039
[9] KOMATSU, H., Ultradistributions, II The kernel theorem and ultradistributions with support in a submanifold, J. Fac. Sc. Univ. Tokyo24, S. 607-628, (1977) · Zbl 0385.46027
[10] LEVIN, B. J., Nullstellenverteilung ganzer Funktionen, Akademie-Verlag, Berlin 1962 · Zbl 0111.07301
[11] LOJASIEWICZ, S., Sur le problème de la division, Stud. Math.18, S. 87-136, 1959
[12] MALGRANGE, B., Ideals of Differentiable Functions, Oxford University Press 1966 · Zbl 0177.17902
[13] NEYMARK, M., On the Laplace transform of functionals on classes of infinitely differentiable functions, Ark. Mat.7, S. 577-594, 1969 · Zbl 0172.42101 · doi:10.1007/BF02590896
[14] NÜRNBERGER, G., Dualität von Schnitten für die metrische Projektion und von Fortsetzungen kompakter Operatoren, Dissertation, Erlangen 1975
[15] PETZSCHE, H.-J., Darstellung der Ultradistributionen vom Beurlingschen und Roumieuschen Typ durch Randwerte holomorpher Funktionen, Dissertation, Düsseldorf 1976
[16] ROUMIEU, C., Sur quelques extensions de la notation de distribution Ann. Sci. Ecole Norm. Sup. Paris, 3 sér,77, S. 41-121, (1960) · Zbl 0104.33403
[17] ROUMIEU, C., Ultra-distributions definies sur Rn et sur certaines classes de variétés differentiables, J. Anal. Math.10, S. 153-192, (1962-63) · Zbl 0122.34802 · doi:10.1007/BF02790307
[18] RUDIN, W., Division in Algebras of Infinitely Differentiable Functions, J. Math. Mech.11, No. 5, S. 797-809, (1962) · Zbl 0199.44201
[19] SCHWARTZ, L., Théorie des Distributions, 3 éd, Hermann, Paris 1966
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