Skip to main content
Log in

Ultradifferentiable functions and Fourier analysis

  • Published:
Results in Mathematics Aims and scope Submit manuscript

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.

Institutional subscriptions

References

  1. A. Beurling: Quasi-analyticity and general distributions. Lectures 4. and 5. AMS Summer Institute, Stanford (1961).

  2. G. Björck: Linear partial differential operators and generalized distributions. Ark. Mat. 6 (1965), 351–407.

    Article  Google Scholar 

  3. J. Bonet, R. W. Braun, R. Meise, B. A. Taylor: Whitney's extension theorem for non-quasianalytic classes of ultradifferentiable functions. Manuscript.

  4. J. Bonet, R. Meise, B. A. Taylor: Whitney's extension theorem for ultradifferentiable functions of Roumieu type. Proc. R. Ir. Acad. 89A (1989), 53–66.

    MathSciNet  Google Scholar 

  5. R. W. Braun, R. Meise: Generalized Fourier expansions for zero-solutions of surjective convolution operators on \({\cal D}_{\lbrace w\rbrace}({\rm R}) \prime\). Arch. Math., to appear.

  6. R. W. Braun, R. Meise, D. Vogt: Existence of fundamental solutions and surjectivity of convolution operators on classes of ultradifferentiable functions. Proc. London Math. Soc., to appear.

  7. R. W. Braun, R. Meise, D. Vogt: Application of the projective limit functor to convolution and partial differential equations. In “Advances in the Theory of Fréchet Spaces” (ed. T. Terzioğlu), NATO ASI Series C 287, Kluwer, Dordrecht-Boston-London 1989, 29–46.

  8. C.-C. Chou: La transformation de Fourier complexe et l'équation de convolution. LNM 325, Springer, Berlin-Heidelberg-New York 1973.

  9. I. Cioranescu, L. Zsidó: ω-ultradistributions and their applications to operator theory. In “Spectral Theory”, Banach Center Publications 8, Warsaw 1982, 77–220.

  10. U. Franken: Kerne von Faltungsoperatoren auf Räumen von Ultradistributionen. Diplomarbeit, Düsseldorf 1988.

    Google Scholar 

  11. U. Franken, R. Meise: Generalized Fourier expansions for ultradistributional solutions of homogeneous convolution equations. Manuscript.

  12. A. Grothendieck: Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. 16, Providence 1955 (reprint 1966).

  13. L. Hörmander: The Analysis of Linear Partial Differential Operators I. Grundlehren 256, Springer, Berlin-Heidelberg-New York-Tokyo 1983.

  14. H. Komatsu: Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Tokyo Sec. IA 20 (1973), 25–105.

    MathSciNet  MATH  Google Scholar 

  15. H. Komatsu: Ultradistributions II. The kernel theorem and ultradistributions with support in a submanifold. J. Fac. Sci. Tokyo Sec. IA 24 (1977), 607–628.

    MathSciNet  MATH  Google Scholar 

  16. G. Köthe: Topological Vector Spaces II. Grundlehren 237, Springer, New York-Heidelberg-Berlin 1979.

  17. J. L. Lions, E. Magenes: Problèmes aux limites non homogènes et applications, Vol. 3. Dunod, Paris 1970.

    MATH  Google Scholar 

  18. R. Meise: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals. J. reine angew. Math. 363 (1985), 59–95.

    MathSciNet  MATH  Google Scholar 

  19. R. Meise: Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type. Studia math. 92 (1989), 211–230.

    MathSciNet  MATH  Google Scholar 

  20. R. Meise, K. Schwerdtfeger, B. A. Taylor: On kernels of slowly decreasing convolution operators. Doğa Tr. J. Math. 10 (1986), 176–197.

    MATH  Google Scholar 

  21. R. Meise, B. A. Taylor: Whitney's extension theorem for ultradifferentiable functions of Beurling type. Ark. Mat. 26 (1988), 265–287.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. Meise, B. A. Taylor: Linear extension operators for ultradifferentiable functions of Beurling type on compact sets. Amer. J. Math. 111 (1989), 309–337.

    Article  MathSciNet  MATH  Google Scholar 

  23. T. Meyer: Die Fourier-Laplace-Transformation quasi-analytischer Funktionale und ihre Anwendung auf Faltungsoperatoren. Diplomarbeit, Düsseldorf 1989.

    Google Scholar 

  24. H. J. Petzsche, D. Vogt: Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions. Math. Ann. 267 (1984), 17–35.

    Article  MathSciNet  MATH  Google Scholar 

  25. C. Roumieu: Sur quelques extensions de la notion de distributions. Ann. Sci. Ecole Norm. Sup. Paris, 3 Sér. 77 (1960), 41–121.

    MathSciNet  MATH  Google Scholar 

  26. L. Schwartz: Théorie des distributions à valeurs vectorielles. Ann. Inst. Fourier (Grenoble) 7 (1957), 1–142.

    Article  MathSciNet  MATH  Google Scholar 

  27. D. Vogt: Sequence space representations of spaces of test functions and distributions. In “Functional analysis, holomorphy, and approximation theory” (ed. G. I. Zapata), Lect. Notes in Pure and Appl. Math. 83, M. Dekker, New York 1983, 405–443.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Braun, R.W., Meise, R. & Taylor, B.A. Ultradifferentiable functions and Fourier analysis. Results. Math. 17, 206–237 (1990). https://doi.org/10.1007/BF03322459

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322459

Keywords

Navigation