Geodesic
Estimate for the least positive root of the harmonic function in a circle decomposed into sine series
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2023), pp. 15-23 
T. Yu. Semenova. Estimate for the least positive root of the harmonic function in a circle decomposed into sine series. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2023), pp. 15-23. http://geodesic.mathdoc.fr/item/VMUMM_2023_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of finding the smallest positive zero of a sine series of a harmonic function in a circle, represented on the boundary of the circle as a series with monotone coefficients, is solved.

[1] Pak I.N., “O summakh trigonometricheskikh ryadov”, Uspekhi matem. nauk, 35:2 (212) (1980), 91–144 | MR | Zbl

[2] Hartman Ph., Wintner A., “On sine series with monotone coefficients”, J. London Math. Soc., 28 (1953), 102–104 | DOI | MR | Zbl

[3] Zigmund A., Trigonometricheskie ryady, Mir, M., 1965

[4] Khardi G.G., Rogozinskii V.V., Ryady Fure, Librokom, M., 2009

[5] Vietoris L., “Über das Vorzeichen gewisser trigonometrischer Summen”, Österr. Acad. Wiss. Math.-Natur. Kl., S.-Ber., Abt. II, 167 (1958), 125–135 | MR | Zbl

[6] Belov A.S., “O primerakh trigonometricheskikh ryadov s neotritsatelnymi chastnymi summami”, Matem. sb., 186:4 (1995), 21–46 | MR | Zbl

[7] Popov A.Yu., “Otsenki naibolshego polozhitelnogo kornya summy ryada po sinusam s monotonnymi koeffitsientami”, Matem. zametki, 96:5 (2014), 747–761 | DOI | Zbl