On a Tauberian theorem for Euler summability.
On a theorem of W. Meyer-König and H. Tietz.
On Conjugate pi-variation and the Coefficients of Power Series
On Multidimensional Generalizations Of Regularly Varying Functions And Tauberian And Abelian Theorems
On Tauberian constants for the summability
On the Laplace Transforms of Logconcave Densities
On the Tauberian constant in the Ikehara theorem
On the value of a distribution at a point
On Valiron and Circle Convergence.
Ordinary convergence follows from statistical summability (C,1) in the case of slowly decreasing or oscillating sequences
Schmidt’s Tauberian theorem says that if a sequence (xk) of real numbers is slowly decreasing and , then . The notion of slow decrease includes Hardy’s two-sided as well as Landau’s one-sided Tauberian conditions as special cases. We show that ordinary summability (C,1) can be replaced by the weaker assumption of statistical summability (C,1) in Schmidt’s theorem. Two recent theorems of Fridy and Khan are also corollaries of our Theorems 1 and 2. In the Appendix, we present a new proof of Vijayaraghavan’s...
O-Regularly Varying Convergence Moduli of Fourier and Fourier-Stieltjes Series.