Structure of Taylor coefficients by equivalence of Tauberian conditions

• Autorzy: Canak I.
• Języki publikacji: EN

Abstrakty

EN

From the equivalent statement of a sequence (un) whose general control modulo of the oscillatory behavior of integer order m is (C, 1) slowly oscillating, we obtain some conclusions regarding the structure of the general control modulo of the oscillatory behavior of integer order k, k < m of (un) and investigate subsequential convergence of some sequences related to (un).

Słowa kluczowe

EN

Taylor coefficients; Tauberian conditions; equivalence; general control modulo

PL

współczynnik Taylora; warunek Tauberiana; równoważność

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 2
• Strony: 309--315
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Canak I.

• Department of Mathematics Adnan Menderes University 09010 Aydin, Turkey,

Bibliografia

• [1] V. G. Avakumović, Sur une extensions de la condition de convergence des theorems inverses de sommabilite, Zbl 0011.20702, C. R. Acad. Sci. Paris 200 (1935), 1515-1517.
• [2] İ. Çanak, M. Dik, F. Dik, On a theorem of W. Meyer-König and H. Tietz, Int. J. Math. Math. Sci. 15 (2005), 2491-2496, MR2184487.
• [3] İ. Çanak, M. Dik, F. Dik, Conditions for convergence and subsequential convergence, MR2246173, App. Math. Letter, 19 (10) (2006), 1042-1045.
• [4] İ. Çanak, Ü. Totur, A Tauberian theorem with a generalized one-sided condition, Abstract and Applied Analyis, vol. 2007, Article ID 60360, 2007, 12 pages.
• [5] İ. Çanak, Ü. Totur, Tauberian theorems for Abel limitability method, to appear in Centr. Eur. J. Math.
• [6] F. Dik, Tauberian theorems for convergence and subsequential convergence of sequences with controlled oscillatory behavior, Zbl 1047.40005, Math. Morav. 5 (2001), 19-56.
• [7] M. Dik, Tauberian theorems for sequences with moderately oscillatory control modulo, Zbl 1046.40004, Math. Morav. 5 (2001), 57-94.
• [8] G. H. Hardy, J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet's series whose coeffients are positive, JFM 45.0389.02, Proc. London Math. Soc. 2 (13) (1913/14), 174-191.
• [9] F. Riesz, Über eine Verallgemeinerung der Parsevalschen Formel, JFM 49.0292.03, Math. Z. 18 (1923), 117-124.
• [10] W. Rudin, Real and Complex Analysis, 3rded., New York, McGraw-Hill, 1987.
• [11] Vera B. Stanojević, Fourier and trigonometric transforms with complex coefficients regularly varying in mean, MR1277833, Fourier analysis, Lect. Notes Pure Appl.Math. 157, Marcel Dekker, New York, 1994.
• [12] Vera B. Stanojević, Tauberian conditions and structures of Taylor and Fourier coefficients, MR1396118, Publ. Inst. Math., Nouv. Ser. 58 (72) (1995), 101-105.
• [13] C. V. Stanojević, Analysis of divergence: control and management of divergent processes, Graduate Research Seminar Lecture Notes, (İ. Çanak, ed.), University of Missouri-Rolla, 1998.
• [14] C. V. Stanojević, Analysis of Divergence: Applications to the Tauberian Theory, Graduate Research Seminar, University of Missouri-Rolla, 1999.