On the invariance of classes \Phi BV, \Lambda BV under composition

On the invariance of classes \Phi BV, \Lambda BV under composition

The necessary and sufficient condition for g \circ f to be in the class \Phi BV, \Lambda BV for every f of that class whose range is in the domain of g is that g be in \operatorname{Lip}1.

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Veröffentlicht in:Proceedings of the American Mathematical Society 2004-03, Vol.132 (3), p.755-760
Hauptverfasser: Pierce, Pamela B., Waterman, Daniel
Format: Artikel
Sprache:eng
Schlagworte:
Abstracting
Continuous functions
Fourier series
Integers
Mathematical functions
Mathematical intervals
Mathematical theorems
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Zusammenfassung:The necessary and sufficient condition for g \circ f to be in the class \Phi BV, \Lambda BV for every f of that class whose range is in the domain of g is that g be in \operatorname{Lip}1.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-03-07129-6