Geodesic
On the absolute convergence of double Fourier series of uniform almost-periodic functions in a uniform metric
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 65-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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Sufficient conditions for the absolute convergence of double Fourier series of uniform almost periodic functions are investigated in the paper in the case when the Fourier exponents have a single limit point at zero. As a structural characteristic of the function under consideration, we use the value built on the basis of the Laplace transform.
Keywords: almost-periodic functions, double Fourier series, function spectrum, limit point at zero
Mots-clés : Fourier coefficients, Laplace transform. 
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     title = {On the absolute convergence of double {Fourier} series of uniform almost-periodic functions in a uniform metric},
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F. M. Talbakov. On the absolute convergence of double Fourier series of uniform almost-periodic functions in a uniform metric. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 65-75. http://geodesic.mathdoc.fr/item/IVM_2023_4_a5/

[1] Besicovich A.S., Almost periodic functions, Cembrige univerity press, 1932 | MR

[2] Bor G., Pochti periodicheskie funktsii, Gos. tekhn.-teoretich. izd., M., 1934

[3] Levitan B.M., Pochti-periodicheskie funktsii, Gos. tekhn.-teoretich. izd., M., 1953 | MR

[4] Bredikhina E.A., “Ob absolyutnoi skhodimosti ryadov Fure pochti-periodicheskikh funktsii”, DAN SSSR, 179:5 (1968), 1023–1026 | Zbl

[5] Bredikhina E.A., “Nekotorye otsenki otklonenii chastnykh summ ryadov Fure ot pochti-periodicheskikh funktsii”, Matem. sb., 50:3 (1960), 369–382 | MR

[6] Musielak J.O., “O bezwzglednej zbieznosci czeregow Fouriera pewnych funcji prawie okresowich”, Bull. Acad. Polon. Sci. Cl., 3:5 (1957), 9–17

[7] Kuptsov N.P., “Ob absolyutnoi i ravnomernoi skhodimosti ryadov Fure pochti-periodicheskikh funktsii”, Matem. sb., 40:2 (1956), 157–178

[8] Pritula Ya.G., “Pro absolyutnu zbizhnist ryadiv Fure maizhe periodichnykh funktsii”, Visn. Lviv. un-tu, 137:5 (1971), 72-80

[9] Dzhafarov A.S., Mamedov G.A., “Ob absolyutnoi skhodimosti ryadov Fure pochti-periodicheskikh funktsii Bezikovicha”, Izv. AN Azerb. SSCR, 1983, no. 5, 8–13 | Zbl

[10] Khasanov Yu.Kh., “Absolyutnaya skhodimost ryadov Fure pochti-periodicheskikh funktsii”, Matem. zametki, 94:5 (2013), 745–756 | DOI | Zbl

[11] Khasanov Yu.Kh., Talbakov F.M., “Ob absolyutnoi skhodimosti ryadov Fure pochti-periodicheskikh funktsii Bezikovicha”, DAN RT, 61:11–12 (2018), 813–821

[12] Talbakov F.M., “Ob absolyutnoi skhodimosti ryadov Fure pochti-periodicheskikh funktsii v ravnomernoi metrike”, DAN RT, 63:5–6 (2020), 289–293

[13] Dyachenko M.I., “O skhodimosti dvoinykh trigonometricheskikh ryadov i ryadov Fure s monotonnymi koeffitsientami”, Matem. sb., 129:1 (1986), 55–72