On the convergence of Fourier series of computable Lebesgue integrable functions
On the convergence of Fourier series of computable Lebesgue integrable functions
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 …