Composing functions of bounded variation

Josephy, Michael

doi:10.1090/S0002-9939-1981-0624930-9

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

Composing functions of bounded variation
HTML articles powered by AMS MathViewer

by Michael Josephy PDF

Proc. Amer. Math. Soc. 83 (1981), 354-356 Request permission

Abstract:

We find necessary and sufficient conditions on $g$ such that $f \circ g({\text {resp}}{\text {.}}g \circ f)$ is a function of bounded variation for all $f$ of bounded variation.

References

Milton Chaika and Daniel Waterman, On the invariance of certain classes of functions under composition, Proc. Amer. Math. Soc. 43 (1974), 345–348. MR 330367, DOI 10.1090/S0002-9939-1974-0330367-9