Mots-clés : harmonic variation
@article{IVM_2023_5_a4,
author = {A. A. Kelzon},
title = {Determination of the jump of a function of $m$-harmonic bounded variation by its {Fourier} series},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {41--47},
year = {2023},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2023_5_a4/}
}
A. A. Kelzon. Determination of the jump of a function of $m$-harmonic bounded variation by its Fourier series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 41-47. http://geodesic.mathdoc.fr/item/IVM_2023_5_a4/
[1] Kelzon A.A., “O funktsiyakh $(m,\Phi )$-ogranichennoi variatsii”, Dokl. AN SSSR, 321:4 (1991), 670–672 | Zbl
[2] Kelzon A.A., “Funktsii $(m,\Phi )$-ogranichennoi variatsii i skhodimost ryadov Fure”, Izv. vuzov. Matem., 1994, no. 8, 29–38 | MR | Zbl
[3] Waterman D., “On convergence of Fourier series of functions of generalized bounded variation”, Studia Math., 44:2 (1972), 107–117 | DOI | MR | Zbl
[4] Avdispahić M., “On the determination of the jump of a function by its Fourier series”, Acta Math. Hungar., 48:3–4 (1986), 267–271 | DOI | MR | Zbl
[5] Kvernadze G., “Determination of the jumps of a bounded function by its Fourier series”, J. Approx. Theory, 92:2 (1998), 167–190 | DOI | MR | Zbl
[6] Fejér L., “Über die Bestimmung des Sprunges der Funktion aus Fourier-reihe”, J. Reine Angew. Math., 142:1 (1912), 165–188 | MR
[7] Czillag P., “Über die Fourierkonstanten einer Funktion von Beschränkter Schwankung”, Mat. Phys. Lapok, 27 (1918), 301–308
[8] Golubov B. I., “Opredelenie skachka funktsii ogranichennoi $p$-variatsii po ee ryadu Fure”, Matem. zametki, 12:1 (1972), 19–28 | Zbl
[9] Kelzon A. A., “Ob opredelenii skachka funktsii obobschennoi ogranichennoi variatsii cherez proizvodnye ot chastnykh summ ee ryada Fure”, Matem. zametki, 99:1 (2016), 35–41 | DOI | MR | Zbl
[10] Fikhtengolts G.M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Lan, SPb., 1997
[11] Bari N.K., Trigonometricheskie ryady, Fizmatgiz, M., 1961
[12] Natanson I.P., Konstruktivnaya teoriya funktsii, GITTL, M., 1949 | MR