Geodesic
Absolute summability of orthogonal series by Euler’s method
Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 51-56

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We have obtained a sufficient condition for the absolute summability of an orthogonal series by the $(E,1)$ method. We have proved that if the coefficients of the orthogonal series decrease monotonically in absolute value, then the condition we have found is exact. We have shown that for coefficients decreasing not necessarily monotonically the condition given is not exact. 
@article{MZM_1977_21_1_a5,
     author = {V. N. Spevakov and A. B. Kudryavtsev},
     title = {Absolute summability of orthogonal series by {Euler{\textquoteright}s} method},
     journal = {Matemati\v{c}eskie zametki},
     pages = {51--56},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a5/}
}
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V. N. Spevakov; A. B. Kudryavtsev. Absolute summability of orthogonal series by Euler’s method. Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 51-56. http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a5/