Abstract
It is proved, that the space of solutions of certain hypoelliptic systems ofp d o, which is determined by projective or inductive growth conditions at ∞, is linear topologically isomorphic to a sequence space. This sequence space may be calculated explicitely for many systems ofp d o and weight conditions.
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References
Baernstein II A.,Representation of holomorphic functions as boundary integrals, Trans. Amer. Math. Soc.160 (1971), 27–37.
Bierstedt K. D., Meise R.,Induktive Limites gewichteter Räume stetiger und holomorpher Funktionen, J. reine angew. Math.282 (1976), 186–220.
Björck G.,Linear partial differential operators and generalized distributions, Ark. Mat.6 (1966), 351–407.
Dragilev M. M.,On regular bases in nuclear spaces, Amer. Soc. Transl. (2)93 (1970), 61–82.
Ehrenpreis L.,Fourier analysis in several complex variables, Wiley Interscience Publ., New York/London/Sidney/Toronto 1970.
Gelfand I. M., Shilov G. E.,Generalized functions, Vol. 2, Academic Press, New York/London 1968.
Hörmander L.,Supports and singular supports of convolutions, Acta Math.110 (1963), 279–302.
Komatsu H.,Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan19 (1967), 366–383.
Langenbruch M.,Isomorphieklassen von Lösungsräumen partieller Differentialgleichungsysteme, Hablitationsschrift Münster 1984.
Langenbruch M.,Darstellung von Distributionen endlicher Ordnung als Randwerte zu hypoelliptischen Differentialoperatoren, Math. Ann.248 (1980), 1–17.
Langenbruch M.,Kolmogorov diameters in solution spaces of systems of partial differential equations, manuscripta math.53 (1985), 35–64.
Langenbruch M.,Bases in solution sheaves of systems of partial differential equations, to appear in J. Reine Angew. Math.
Langenbruch M.,Powerseries spaces and weighted solution spaces of partial differential equations, to appear in Math. Z.
Vogt D.,Sequence space representations of spaces of testfunctions and distributions, Functional analysis, holomorphy and approximation, Proc. Sem. Rio de Janeiro 1979, LN Pure Applied Math.83 (1983), 405–443.
Vogt D.,Ein Isomorphiesatz für Potenzreihenräme, Arch. Math.38 (1982), 540–548.
Vogt D.,Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, manuscripta math.37 (1982), 269–301.
Wiechert G.,Dualitäts- und Strukturtheorie der Kerne von linearen Differentialoperatoren, Dissertation Wuppertal 1982
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Langenbruch, M. Sequence space representations for weighted solution spaces of hypoelliptic systems of partial differential operators. Rend. Circ. Mat. Palermo 35, 169–202 (1986). https://doi.org/10.1007/BF02844730
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DOI: https://doi.org/10.1007/BF02844730