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.
Permanenz- und Taubersätze bei pV-Summierung.
Polynomials of multipartitional type and inverse relations
Chou, Hsu and Shiue gave some applications of Faà di Bruno's formula to characterize inverse relations. Our aim is to develop some inverse relations connected to the multipartitional type polynomials involving to binomial type sequences.
Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces
We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces.
Remark on a theorem of K. M. Slipenčuk in the theory of summability of series
Some applications of Tauberian theorems in probability theory.
Some Tauberian theorems for Euler and Borel summability.
Some Tauberian Theorems for the Circle Family of Summability Methods.
Some Tauberian theorems on summability methods of integrals
Some Tauberian theorems related to operator theory
This article is a survey of some Tauberian theorems obtained recently in connection with work on asymptotic behaviour of semigroups of operators on Banach spaces. The results in operator theory are described in [6], where we made little attempt to show the Tauberian aspects. At the end of this article, we will give a sketch of the connections between the results in this article and in [6]; for details, the reader can turn to the original papers. In this article, we make no attempt to describe...
Statistical extensions of some classical Tauberian theorems in nondiscrete setting
Schmidt’s classical Tauberian theorem says that if a sequence of real numbers is summable (C,1) to a finite limit and slowly decreasing, then it converges to the same limit. In this paper, we prove a nondiscrete version of Schmidt’s theorem in the setting of statistical summability (C,1) of real-valued functions that are slowly decreasing on ℝ ₊. We prove another Tauberian theorem in the case of complex-valued functions that are slowly oscillating on ℝ ₊. In the proofs we make use of two nondiscrete...
Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense.
Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable
We give a sufficient condition for a non-negative random variable to be of Pareto type by investigating the Laplace-Stieltjes transform of the cumulative distribution function. We focus on the relation between the singularity at the real point of the axis of convergence and the asymptotic decay of the tail probability. For the proof of our theorems, we apply Graham-Vaaler’s complex Tauberian theorem. As an application of our theorems, we consider the asymptotic decay of the stationary distribution...
Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws.
Tauberian conditions for a general limitable method.
Tauberian conditions for conull spaces.
Tauberian L1-Convergence Classes of Fourier Series. II.