Generalized Cantor sets and sets of sums of convergent alternating series

• Autorzy: Dindoš M.
• Języki publikacji: EN

Abstrakty

EN

We give a complete characterization of sets of sums of absolutely convergent series with alternating signs. This result finishes works of various authors [3], [4]-[8] who studied this problem. As we will see, the studied sets are exactly sets that can be obtained by generalizing the construction of the Cantor set.

Słowa kluczowe

EN

absolutely convergent series; Cantor sets

PL

absolutnie zbieżny szereg; zbiory Cantor`a

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 1
• Strony: 131--150
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Dindoš M.

• University of North Carolina Phillips Hall CB 3250 Chapel Hill NC 27599 USA

Bibliografia

• [1] Dindoš, M., On a typical senes with alternating signs, Real Anal. Exchange 25(2) (1999/2000), 617-628.
• [2] Dindoš, M., On sign distribution in relatively convergent series, Acta Math. Hun- gar. 91(4) (2001), 283-300 (to appear).
• [3] Menon, P. K., On a class of a perfect set, Bull. Amer. Math. Soc. 54 (1948), 706-711.
• [4] Šalát, T., Absolutely convergent series and dyadic expansions (in Slovak), Math.- Phys. J. Slovak Acad. Sei. 9(1) (1959), 3-14.
• [5] Šalát, T., A note on absolutely convergent series (in Slovak), Math.-Phys. J. Slovak Acad. Sei. 7(3) (1957), 139-142.
• [6] Šalát, T., Absolut konvergente Reihen und das Hausdorffsche Mass, Czechoslovak Math. J. 84(9) (1959), 372-389.
• [7] Šalát, T., On sums of certain convergent series (in Slovak), Math.-Phys. J. Slovak Acad. Sei. 4(4) (1954), 203-211.
• [8] Šalát, T., On certain properties of positive series (in Slovak), Acta Univ. Come- nian. Fac. Rerum Natur. 2 (1957), 71-74.