Statistic D-Property of Voronoi Summation Methods of Class W Q 2
- 19 Downloads
We propose a general method for obtaining Tauberian theorems with remainder for one class of Voronoi summation methods for double sequences of elements of a locally convex, linear topological space. This method is a generalization of the Davydov method of C-points.
KeywordsTopological Space Double Sequence Tauberian Theorem Summation Method Linear Topological Space
Unable to display preview. Download preview PDF.
- 1.A. P. Robertson and W. S. Robertson, Topological Vector Spaces [Russian translation], Mir, Moscow (1967).Google Scholar
- 2.G. A. Mikhalin, “Tauberian theorems with remainder for summation methods of the Hölder and Cesàro types,” Ukr. Mat. Zh., 41, No. 7, 918–923 (1989).Google Scholar
- 3.N. A. Davydov, “On one property of Cesàro methods for summation of series,” Mat. Sb., 38, Issue 4, 509–524 (1956).Google Scholar
- 4.H. Fast, “Sur la convergence statistique,” Colloq. Math., 2, 241–244 (1951).Google Scholar
- 5.M. M. Bilots'kii, S. Ya. Dekanov, and G. O. Mikhalin, “Tauberian theorems with remainder for Voronoi summation methods with rational generating function,” Frakt. Analiz Sumizh. Pytannya, 2, 178–189 (1998).Google Scholar
- 6.M. A. Kalatalova, “(C)-property of the Cesàro methods for summation of double series,” Ukr. Mat. Zh., 23, No. 3, 391–399 (1971).Google Scholar
- 7.V. M. Aldanov and G. O. Mikhalin, “Tauberian theorems with remainder for (H,p,α,β)-and, (C, pα, β)-methods for summation of functions of two variables,” Ukr. Mat. Zh., 51, No. 8, 1036–1044 (1999).Google Scholar