Uniqueness Theorem for Multiple Franklin Series
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 199-210 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents the proof of the uniqueness theorem for multiple series in the Franklin system that converge in measure and whose majorant of cubic partial sums with numbers $2^\nu$ satisfies a certain necessary condition. This result is new in the one-dimensional case as well.
Keywords: multiple series, Franklin system, uniqueness.
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     title = {Uniqueness {Theorem} for {Multiple} {Franklin} {Series}},
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G. G. Gevorkyan. Uniqueness Theorem for Multiple Franklin Series. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 199-210. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a4/

[1] Ph. Franklin, “A set of continuous orthogonal functions”, Math. Ann., 100 (1928), 522–528 | DOI | MR | Zbl

[2] Z. Ciesielski, “Properties of the orthonormal Franklin system”, Studia Math., 23 (1963), 141–157 | MR | Zbl

[3] Z. Ciesielski, “Properties of the orthonormal Franklin system. II”, Studia Math., 27 (1966), 289–323 | MR | Zbl

[4] S. V. Bochkarev, “Some inequalities for the Franklin series”, Anal. Math., 1:4 (1975), 249–257 | DOI | MR | Zbl

[5] P. Wojtaszczyk, “The Franklin system is an unconditional basis in $H^1$”, Ark. Mat., 20:2 (1982), 293–300 | DOI | MR | Zbl

[6] G. G. Gevorkyan, “O ryadakh po sisteme Franklina”, Uch. zap. Erevansk. gos. un-ta. Estestv. nauki, 2 (162) (1986), 146–148 | MR

[7] G. G. Gevorkyan, A. Kamont, “On the uniqueness of series with respect to general Franklin systems”, J. Contemp. Math. Anal., 44:5 (2009), 271–283 | DOI | MR | Zbl

[8] G. G. Gevorkyan, “O edinstvennosti ryadov po sisteme Franklina”, Matem. zametki, 46:2 (1989), 51–58 | MR | Zbl

[9] M. P. Pogosyan, “O edinstvennosti ryadov po obschei sisteme Franklina”, Izv. NAN Armenii. Ser. matem., 35:4 (2000), 75–81

[10] G. G. Gevorkyan, “Mazhoranta i edinstvennost ryadov po sisteme Franklina”, Matem. zametki, 59:4 (1996), 521–545 | DOI | MR | Zbl

[11] G. G. Gevorkyan, “Teoremy edinstvennosti dlya ryadov po sisteme Franklina”, Matem. zametki, 98:5 (2015), 786–789 | DOI | Zbl

[12] M. Gusman, Differentsirovanie integralov v $\mathbb R^n$, Matematika. Novoe v zarubezhnoi nauke, 9, Mir, M., 1978 | MR | Zbl