Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T10:05:57.438Z Has data issue: false hasContentIssue false
  • English
  • Français

On Λ-Ω-extendable distributions

Published online by Cambridge University Press:  24 October 2008

Peter Dierolf
Peter Dierolf
Affiliation:
FB IV – Mathematik der Universität Trier, D-5500 Trier, West Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Let Λ ⊂ Ω ⊂ ℝnbe open subsets. We construct a natural space of test functions on Λ such that the dual consists exactly of those distributions on Λ which can be extended to distributions on Ω. As an application of this representation we calculate the space of multiplication operators on as well as the space of absolutely regular extendable distributions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 135 - 142
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]De Wilde, M.. Closed Graph Theorems and Webbed Spaces. (Pitman, 1978).Google Scholar
[2]Dierolf, P.. Multiplication and convolution operators between spaces of distributions. In Functional Analysis: Surveys and Recent Results, vol. III, ed. Bierstedt, K. D. and Fuchssteiner, B. (North-Holland Publ. Comp., 1984), pp. 305–330.Google Scholar
[3]Dierolf, P.. Some locally convex spaces of regular distributions. Studia Math. 77 (1984), 393–412.CrossRefGoogle Scholar
[4]Dierolf, P. and Voigt, J.. Calculation of the bidual for some function spaces. Integrable distributions. Math. Ann. 253 (1980), 63–87.Google Scholar
[5]Dierolf, S. and Schwanengel, U.. Examples of locally compact non-compact minimal topological groups. Pacific J. Math. 82 (1979), 249–355.CrossRefGoogle Scholar
[6]Floret, K.. Some aspects of the theory of locally convex inductive limits. In Functional Analysis: Surveys and Recent Results, vol. II, ed. Bierstedt, K. D. and Fuchssteiner, B. (North-Holland Publ. Comp., 1980), pp. 205–237.CrossRefGoogle Scholar
[7]Grothendieck, A.. Produits tensoriels topologiques et espaces nucléaires. Memoirs Amer. Math. Soc. 16 (1966).Google Scholar
[8]Horvath, J.. Topological vector spaces and distributions (Addison-Wesley Publishing Company, 1966).Google Scholar
[9]Łojasiewicz, S.. Sur le probleme de division. Studia Math. 18 (1959), 87–136.CrossRefGoogle Scholar
[10]Schwartz, L.. Théorie des distributions à valeurs vectorielles. Ann. Inst. Fourier Grenóble 7 (1957), 1–141.CrossRefGoogle Scholar
[11]Schwartz, L.. Some applications of the theory of distributions. In Lectures on Modern Mathematics, ed. Saaty, T. L. (J. Wiley, 1963), pp. 23–58.Google Scholar
[12]Schwartz, L.. Théorie des distributions (Hermann, 1966).Google Scholar
[13]Valdivia, M.. Sobre el espacio ℬ0(Ω). Rev. Real. Acad. Ci. Exact. Fis. Natur. Madrid 74 (1980), 835–863.Google Scholar
[14]Vogt, D.. Sequence space representations of spaces of test functions and distributions. In Functional Analysis, Holomorphy and Approximation Theory, ed. Zapata, G. I. (Marcel Dekker, 1983).Google Scholar
[15]Voigt, J.. Factorization in some Fréchet algebras of differentiable functions. Studia Math. 77 (1984), 333–348.CrossRefGoogle Scholar