Skip to main content
Log in

Sequence space representations for weighted solution spaces of hypoelliptic systems of partial differential operators

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baernstein II A.,Representation of holomorphic functions as boundary integrals, Trans. Amer. Math. Soc.160 (1971), 27–37.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bierstedt K. D., Meise R.,Induktive Limites gewichteter Räume stetiger und holomorpher Funktionen, J. reine angew. Math.282 (1976), 186–220.

    MATH  MathSciNet  Google Scholar 

  3. Björck G.,Linear partial differential operators and generalized distributions, Ark. Mat.6 (1966), 351–407.

    Article  MATH  MathSciNet  Google Scholar 

  4. Dragilev M. M.,On regular bases in nuclear spaces, Amer. Soc. Transl. (2)93 (1970), 61–82.

    MATH  Google Scholar 

  5. Ehrenpreis L.,Fourier analysis in several complex variables, Wiley Interscience Publ., New York/London/Sidney/Toronto 1970.

    MATH  Google Scholar 

  6. Gelfand I. M., Shilov G. E.,Generalized functions, Vol. 2, Academic Press, New York/London 1968.

    Google Scholar 

  7. Hörmander L.,Supports and singular supports of convolutions, Acta Math.110 (1963), 279–302.

    Article  MATH  MathSciNet  Google Scholar 

  8. Komatsu H.,Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan19 (1967), 366–383.

    Article  MATH  MathSciNet  Google Scholar 

  9. Langenbruch M.,Isomorphieklassen von Lösungsräumen partieller Differentialgleichungsysteme, Hablitationsschrift Münster 1984.

  10. Langenbruch M.,Darstellung von Distributionen endlicher Ordnung als Randwerte zu hypoelliptischen Differentialoperatoren, Math. Ann.248 (1980), 1–17.

    Article  MATH  MathSciNet  Google Scholar 

  11. Langenbruch M.,Kolmogorov diameters in solution spaces of systems of partial differential equations, manuscripta math.53 (1985), 35–64.

    Article  MATH  MathSciNet  Google Scholar 

  12. Langenbruch M.,Bases in solution sheaves of systems of partial differential equations, to appear in J. Reine Angew. Math.

  13. Langenbruch M.,Powerseries spaces and weighted solution spaces of partial differential equations, to appear in Math. Z.

  14. 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.

    MathSciNet  Google Scholar 

  15. Vogt D.,Ein Isomorphiesatz für Potenzreihenräme, Arch. Math.38 (1982), 540–548.

    Article  MATH  MathSciNet  Google Scholar 

  16. Vogt D.,Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, manuscripta math.37 (1982), 269–301.

    Article  MATH  MathSciNet  Google Scholar 

  17. Wiechert G.,Dualitäts- und Strukturtheorie der Kerne von linearen Differentialoperatoren, Dissertation Wuppertal 1982

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02844730

Keywords

Navigation