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The j-Differential and its Integral

Published online by Cambridge University Press:  20 January 2009

W. H. Ingram
W. H. Ingram
Affiliation:
150 Claremont Avenue, New York 27
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The reciprocity, , has been shown to hold when g(x) is in B* [Proc. Edin. Math. Soc., 12 (1960), 85]. The purpose of the present note is to show that it holds more generally and in particular when g(x) is in a subclass B″, of functions of bounded variation B, such that B* ⊂ B″ ⊂ B′ ⊂ B; it is assumed that f(x) is any function in D1 and that f(x) and g(x) are both continuous on the left and possibly with simultaneous points of discontinuity.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 85 - 86
Copyright
Copyright © Edinburgh Mathematical Society 1962