Sherstyukov, V. B. To the question on \(\gamma\)-sufficient sets. (English. Russian original) Zbl 0970.32002 Sib. Math. J. 41, No. 4, 778-784 (2000); translation from Sib. Mat. Zh. 41, No. 4, 935-943 (2000). Weakly sufficient sets, introduced by D. Schneider, play an important role in the questions of representing analytic functions by function series. Their natural generalization, the so-called \(\gamma\)-sufficient sets, were proposed by Yu. Korobeinik who, in particular, applied them to constructing discrete maximum sets in some classes of entire functions (a Levinson-type theorem). The question of interrelation between weakly sufficient sets and (Iyer) effective sets was discussed by Yu. Korobeinik [Russ. Math. Surv. 36, No. 1, 75-137 (1981); translation from Usp. Mat. Nauk 36, No. 1 (21), 73-126 (1981; Zbl 0483.30003)] and completely in A. B. Abanin [Mat. Zametki 40, No. 4, 442-454 (1986; Zbl 0617.46032)].In the article under review, the author uses the method suggested by A. B. Abanin (involving more general results) to solve a similar problem for \(\gamma\)-sufficient sets. Reviewer: V.Grebenev (Novosibirsk) Cited in 3 Documents MSC: 32A15 Entire functions of several complex variables 32K05 Banach analytic manifolds and spaces 32A17 Special families of functions of several complex variables Keywords:space of entire functions; sufficient set; \(\gamma \)-sufficient set; function series Citations:Zbl 0483.30003; Zbl 0625.46030; Zbl 0617.46032 PDFBibTeX XMLCite \textit{V. B. Sherstyukov}, Sib. Math. J. 41, No. 4, 935--943 (2000; Zbl 0970.32002); translation from Sib. Mat. Zh. 41, No. 4, 935--943 (2000) Full Text: DOI EuDML References: [1] Schneider D. M., ”Sufficient sets for some spaces of entire functions,” Trans. Amer. Math. Soc.,197, 161–180 (1974). · Zbl 0264.46018 · doi:10.1090/S0002-9947-1974-0357835-2 [2] Korobeînik Yu. F., ”Representing systems,” Uspekhi Mat. Nauk,36, No. 1, 73–126 (1981). [3] Korobeînik Yu. F., ”Inductive and projective topologies. Sufficient sets and representing systems,” Izv. Akad. Nauk SSSR Ser. Mat.,50, No. 3, 539–565 (1986). [4] Abanin A. V., ”On some criteria for weak sufficiency,” Mat. Zametki,40, No. 4, 442–454 (1986). · Zbl 0617.46032 [5] Korobeînik Yu. F., ”Maximal and {\(\gamma\)}-sufficient sets. Applications to entire functions. I,” in: Function Theory, Functional Analysis, and Some of Their Applications [in Russian], 1990, No. 54, pp. 42–59. · Zbl 0741.30023 [6] Sherstyukov V. B., ”On a certain class of complete systems,” Izv. Vyssh. Uchebn. Zaved. Estestv. Nauki,2, 38–40 (1997). · Zbl 0918.46007 [7] Edwards R. D., Functional Analysis. Theory and Applications [Russian translation], Mir, Moscow (1969). · Zbl 0189.12103 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.