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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
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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
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