Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T09:34:38.282Z Has data issue: false hasContentIssue false
  • English
  • Français

The Linear j-Differential Equation

Published online by Cambridge University Press:  20 January 2009

W. H. Ingram
W. H. Ingram
Affiliation:
City College, New York 31 150 Claremont Ave., New York 27
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.

The basic reciprocity of j-differential and LM-integral

for bounded functions f(x) with simple discontinuities but continuous on the left at each point and for g(x) in the somewhat restricted class B of functions of bounded variation and also left-continuous, was established in (2) and (3); the dot here indicates the lower product of and (jg, g+ (x+)dx), with , and the integral indicated is the RJDS-integral, equivalent to (LM) .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 3 , June 1965 , pp. 211 - 219
Copyright
Copyright Edinburgh Mathematical Society 1965

References

REFERENCES

(1) Hildebrandt, T. H., On systems of linear differentio-Stieltjes integral equations, Illinois J. Math. 3 (1959), 352373.CrossRefGoogle Scholar
(2) Ingram, W. H., The j-differential and its integral, I. Proc. Edin. Math. Soc. (2) 12 (1960), 8593.CrossRefGoogle Scholar
(3) Ingram, W. H., The j-differential and its integral, II, Proc. Edin. Math. Soc. (2) 13 (1962), 8586.CrossRefGoogle Scholar
(4) MacNerney, J. S., Stieltjes integrals in linear spaces, Ann. Math. (2) 61 (1955), 354367.CrossRefGoogle Scholar
(5) MacNerney, J. S., Continuous products in linear spaces, J. Elisha Mitchell Sci. Soc. 71 (1955), 185200.Google Scholar
(6) Wall, H. S., Concerning harmonic matrices, Archiv. der Math. 5 (1954), 160167.CrossRefGoogle Scholar