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On the invariance of classes under composition
Authors:Pamela B Pierce  Daniel Waterman
Institution:Department of Mathematics and Computer Science, The College of Wooster, Wooster, Ohio 44691 ; Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431-0991
Abstract: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 $\operatorname{Lip}1$.

Keywords:Bounded variation  Fourier series
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