Tauberian theorems for Abel limitability method

• Autorzy: İbrahim Çanak , Ümit Totur
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Abel method of limitability; general control modulo; Tauberian conditions; slow oscillation; moderate oscillation; subsequential convergence

Kategorie tematyczne

• 40G10: Abel, Borel and power series methods
• 40E05: Tauberian theorems, general

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 301-306

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

İbrahim Çanak

• Adnan Menderes University

autor

Ümit Totur

• Adnan Menderes University

Bibliografia

• [1] Çanak İ., Totur Ü., A Tauberian theorem with a generalized one-sided condition, Abstr. Appl. Anal., 2007, 60360
• [2] Dik F., Tauberian theorems for convergence and subsequential convergence of sequences with controlled oscillatory behavior, Math. Morav., 2001, 5, 19–56
• [3] Dik M., Tauberian theorems for sequences with moderately oscillatory control moduli, Math. Morav., 2001, 5, 57–94
• [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
• [5] Rényi A., On a Tauberian theorem of O. Szász, Acta Univ. Szeged Sect. Sci. Math., 1946, 11, 119–123
• [6] Schmidt R., Über divergente folgen und lineare mittelbildungen, Math. Z., 1925, 22, 89–152 http://dx.doi.org/10.1007/BF01479600
• [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
• [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

Identyfikatory

DOI

10.2478/s11533-008-0019-7