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- W1624552139 abstract "This 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." @default.
- W1624552139 created "2016-06-24" @default.
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- W1624552139 date "2006-08-28" @default.
- W1624552139 modified "2023-09-27" @default.
- W1624552139 title "Lp Computable Functions and Fourier Series" @default.
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