Geodesic
On the density of convergent subsequences of orthogonal series
Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 419-428.

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A necessary and sufficient condition for $\omega(n)$ to be a Weyl factor for the existence, almost everywhere, of convergent subsequences of partial sums of an orthogonal series with upper density one is established. 
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     author = {N. L. Lebedeva},
     title = {On the density of convergent subsequences of orthogonal series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {419--428},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a3/}
}
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N. L. Lebedeva. On the density of convergent subsequences of orthogonal series. Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 419-428. http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a3/