Tauberian theorems for Abel limitability method
İbrahim Çanak ; Ümit Totur
Open Mathematics, Tome 6 (2008), p. 301-306 / Harvested from The Polish Digital Mathematics Library

This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:269023
@article{bwmeta1.element.doi-10_2478_s11533-008-0019-7,
     author = {\.Ibrahim \c Canak and \"Umit Totur},
     title = {Tauberian theorems for Abel limitability method},
     journal = {Open Mathematics},
     volume = {6},
     year = {2008},
     pages = {301-306},
     zbl = {1162.40003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0019-7}
}
İbrahim Çanak; Ümit Totur. Tauberian theorems for Abel limitability method. Open Mathematics, Tome 6 (2008) pp. 301-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0019-7/

[1] Çanak İ., Totur Ü., A Tauberian theorem with a generalized one-sided condition, Abstr. Appl. Anal., 2007, 60360 | Zbl 1155.40304

[2] Dik F., Tauberian theorems for convergence and subsequential convergence of sequences with controlled oscillatory behavior, Math. Morav., 2001, 5, 19–56 | Zbl 1047.40005

[3] Dik M., Tauberian theorems for sequences with moderately oscillatory control moduli, Math. Morav., 2001, 5, 57–94 | Zbl 1046.40004

[4] Littlewood J.E., The converse of Abel’s theorem on power series, Proc. London Math. Soc., 1910, 9, 434–448 http://dx.doi.org/10.1112/plms/s2-9.1.434 | Zbl 42.0276.01

[5] Rényi A., On a Tauberian theorem of O. Szász, Acta Univ. Szeged Sect. Sci. Math., 1946, 11, 119–123 | Zbl 0060.15703

[6] Schmidt R., Über divergente folgen und lineare mittelbildungen, Math. Z., 1925, 22, 89–152 http://dx.doi.org/10.1007/BF01479600 | Zbl 51.0182.04

[7] Stanojević Č.V., Analysis of Divergence: Control and Management of Divergent Process, Graduate Research Seminar Lecture Notes (Edited by İ. Çanak), University of Missouri-Rolla, 1998

[8] Stanojević Č.V., Analysis of Divergence: Applications to the Tauberian Theory, Graduate Research Seminar, University of Missouri - Rolla, 1999

[9] Stanojević Č.V., Stanojević V.B., Tauberian retrieval theory, Publ. Inst. Math., 2002, 71, 105–111 http://dx.doi.org/10.2298/PIM0271105S | Zbl 1027.40005

[10] Tauber A., Ein Satz aus der Theorie der unendlichen Reihen, Monatsh. Math. Phys., 1897, 8, 273–277 http://dx.doi.org/10.1007/BF01696278