Lp Computable Functions and Fourier Series

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dc.creatorMoser, Philippe
dc.date2006-08-28
dc.date2007-05-11
dc.date.accessioned2026-07-07T08:00:46Z
dc.date.available2026-07-07T08:00:46Z
dc.descriptionThis paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp-computable functions (computable Lebesgue integrable functions) with a size notion, by introducing Lp-computable Baire categories. We show that Lp-computable Baire categories satisfy the following three basic properties. Singleton sets {f} (where f is Lp-computable) are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp-computable functions is not meager. We give an alternative characterization of meager sets via Banach Mazur games. We study the convergence of Fourier series for Lp-computable functions and show that whereas for every p>1, the Fourier series of every Lp-computable function f converges to f in the Lp norm, the set of L1-computable functions whose Fourier series does not diverge almost everywhere is meager.
dc.descriptioncorrected abstract
dc.identifierhttps://arxiv.org/abs/cs/0608106
dc.identifierhttp://arxiv.org/abs/cs/0608106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128752
dc.subjectComputational Complexity
dc.titleLp Computable Functions and Fourier Series
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