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• W2896652933 abstract "For a separable finite diffuse measure space $mathcal{M}$ and an orthonormal basis ${varphi_n}$ of $L^2(mathcal{M})$ consisting of bounded functions $varphi_nin L^infty(mathcal{M})$, we find a measurable subset $Esubsetmathcal{M}$ of arbitrarily small complement $|mathcal{M}setminus E|<epsilon$, such that every measurable function $fin L^1(mathcal{M})$ has an approximant $gin L^1(mathcal{M})$ with $g=f$ on $E$ and the Fourier series of $g$ converges to $g$, and a few further properties. The subset $E$ is universal in the sense that it does not depend on the function $f$ to be approximated. Further in the paper this result is adapted to the case of $mathcal{M}=G/H$ being a homogeneous space of an infinite compact second countable Hausdorff group. As a useful illustration the case of $n$-spheres with spherical harmonics is discussed. The construction of the subset $E$ and approximant $g$ is sketched briefly at the end of the paper." @default.
• W2896652933 created "2018-10-26" @default.
• W2896652933 creator A5014446077 @default.
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• W2896652933 date "2018-10-14" @default.
• W2896652933 modified "2023-09-26" @default.
• W2896652933 title "Approximations in $L^1$ with convergent Fourier series" @default.
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• W2896652933 hasPublicationYear "2018" @default.
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