Geodesic
$\alpha$-monotone sequences and the Lorentz theorem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2023), pp. 63-67 
E. D. Alferova; M. I. Dyachenko. $\alpha$-monotone sequences and the Lorentz theorem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2023), pp. 63-67. http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a7/
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     author = {E. D. Alferova and M. I. Dyachenko},
     title = {$\alpha$-monotone sequences and the {Lorentz} theorem},
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     pages = {63--67},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_2_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Properties of $\alpha$-monotone sequences are studied. A relationship between $\alpha$-monotonicity and the limiting rate of change of coefficients is revealed. Operations on sequences that do not lead out of the class $M_\alpha$ are discussed. An analogue of the Lorentz theorem for trigonometric series with coefficients from the classes $M_\alpha$ for $0 <\alpha <1$ is proved.

[1] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965

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[4] Dyachenko M.I., “Asimptotika summ kosinus-ryadov s koeffitsientami drobnoi monotonnosti”, Matem. zametki, 110:6 (2021), 865–874 | DOI | Zbl

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