Geodesic
On the convergence of greedy approximants of trigonometric Fourier series
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 132-144

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Efficient versions of the Cauchy criterion for the convergence in $L_p$ of greedy approximants of trigonometric Fourier series are discussed. 
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     author = {S. V. Konyagin},
     title = {On the convergence of greedy approximants of trigonometric {Fourier} series},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a11/}
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S. V. Konyagin. On the convergence of greedy approximants of trigonometric Fourier series. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 132-144. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a11/