Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T09:41:23.721Z Has data issue: false hasContentIssue false
  • English
  • Français

On the integral representation of the endomorphisms of Mikuśinski's operator field

Published online by Cambridge University Press:  20 January 2009

András Bleyer
András Bleyer
Affiliation:
Budapest, Hungary
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We proved in (1) that every continuous endomorphism can be generated on a subring of the field M. More precisely, the ring H of piecewise polynomial functions has the property that every isomorphism from H into M, continuous in the sequential topology of H, can be extended to a continuous endomorphism of M where the notion of continuity in M is the usual sequential one.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 4 , December 1971 , pp. 351 - 367
Copyright
Copyright © Edinburgh Mathematical Society 1971

References

REFERENCES

(1) Bleyer, A., On continuous endomorphisms of Mikusinśki's operator field, Acta Math. Acad. Sci. Hungar. 21 (3–4) (1970), 393–402.Google Scholar
(2)Boehme, T. K., On sequences of continuous functions and convolution, Studia Math. 25 (1965), 333–335.Google Scholar
(3) Ditkin, V. A. and Prudinkov, A. P., Integral transforms and operational calculus (Pergamon Press, 1965).Google Scholar
(4) Efros, A. M., On some applications of operational calculus to analysis (in Russian), Mat. Sb. 42 (1935).Google Scholar
(5) Erdélyi, A., Operational calculus and generalized functions (New York, 1963).Google Scholar
(6) Gesztelyi, E., Über das Stieltjes-Integral von Operatorfunktionen II, Publ. Math. Debrecen 13 (1966), 313–324.Google Scholar
(7) Gesztelyi, E., Über lineare Operatortransformation, Publ. Math. Debrecen 14 (1967), 169–206.CrossRefGoogle Scholar
(8) Máté, L., Note on Mikusinśki's logarithm, Bull. Acad. Polon. Sci. Ser. Sci. Math. 13 (1965), 641–644.Google Scholar
(9) Mikusinśki, J., Operational calculus (New York, 1959).Google Scholar
(10) Mikusinśki, J., An approximation theorem and its application, Studia Math. 27 (1966), 141–145.Google Scholar
(11) Stopp, F., Zur funktiontheoretischen Auffassung der Mikusinśkischen Operatorenrechnung, Math. Nachr. 32 (1966), 187–205.Google Scholar