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Smoothness conditions and integrability theorems on bounded Vilenkin groups
Published online by Cambridge University Press: 09 April 2009
Abstract
Various criteria, in terms of forward differences and related operations on coefficients, are shown to imply that certain series on bounded Vilenkin groups represent integrable functions. These results include analogues of known integrability theorems for trigonometric series. The method of proof is to pass from the given series to a derived series, and to deduce the integrability of the original series from smoothness properties of the latter.
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- Copyright © Australian Mathematical Society 1988
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