Geodesic
On recovery of a Franklin series from its sum
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 151-157.

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In an earlier work of author a theorem on recovery of Franklin series from its sum under some conditions was obtained. In present article it is shown that to some extent these conditions are necessary.
Keywords: Franklin series, uniqueness, AH-integral.
Mots-clés : majorant 
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K. A. Kerian. On recovery of a Franklin series from its sum. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 151-157. http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a2/

[1] Ph. Franklin, “A Set of Continuous Orthogonal Functions”, Math. Ann., 100 (1928), 522–528 | DOI | MR

[2] K.A. Keryan, “Uniqueness Theorem for Franklin Series”, J. of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 52:2 (2017), 92–101 | MR | Zbl

[3] K.A. Keryan, “Uniqueness Theorem for Additive Functions and its Applications to Orthogonal Series”, Mathematical Notes, 97:3 (2015), 362–375 | DOI | MR | Zbl

[4] G. G. Gevorkyan, “Uniqueness of Franklin Series”, Mathematical Notes of the Academy of Sciences of the USSR, 46:2 (1989), 609–615 | DOI | MR | Zbl

[5] G. G. Gevorkyan, “Unboundedness of the Shift Operator with Respect to the Franklin System in the Space $L_1$”, Mathematical Notes of the Academy of Sciences of the USSR, 38:4 (1985), 796–802 | MR | Zbl