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Construction of Primitives of Generalized Derivatives with Applications to Trigonometric Series

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen
P. S. Bullen*
Affiliation:
University of British Columbia
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This paper is an extension of the ideas discussed in (3, §§ 14-16); the extension consisting of the use of the third and fourth symmetric Riemann derivative instead of the Schwarz or second symmetric Riemann derivative.

The J2integral, due to James (1), is defined in (3) as follows. Let f(x) be measurable on [a, b] and finite at each point; if there exists a continuous function F(x) such that D2F = f everywhere on (a, b),

then

1.1

The definition is unique since if F(x) and G(x) are continuous and D2F =D2G everywhere then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 48 - 58
Copyright
Copyright © Canadian Mathematical Society 1961

References

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