Tauberian theorems for Abel limitability method

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

Some Tauberian theorems for Borel summability methods

We investigate the conditions needed for a Borel summable sequence to be convergent. The results of this paper extend and improve the well-known result of Hardy and Littlewood (1913) [1].     

Abelian and Tauberian theorems for a class of integral transforms

Extending the Wiener-Ganelius method we give Abelian and precise Tauberian remainder results for a class of Fourier kernels which includes the Hankel transform $\text{?(x) = ∫}{}_0{}^{\mathrm{\infty }}\text{√xu J}{}_{\mathrm{r}}\text{(xu) ?(u) du, v ? ?}\text{1}\text{2}$. Further, we discuss applications to Fourier series and integrals.     

Dominated variation and related concepts and Tauberian theorems for Laplace transforms

Some Abelian and Tauberian theorems are proved under conditions of dominated variation and related concepts. For example U is dominatedly varying if and only if its Laplace-Stieltjes transform is dominatedly varying.     

One-sided Tauberian conditions and double sequences

We give a theorem of Vijayaraghavan type for summability methods for double sequences, which allows a conclusion from boundedness in a mean and a one-sided Tauberian condition to the boundedness of the sequence itself. We apply the result to certain power series methods for double sequences improving a recent Tauberian result by S. Baron and the author [4]. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tauberian theorems for absolute summability

Ohne ZusammenfassungHerrn A.Ostrowski zum 60. Geburtstag gewidmetThis work has been completed while the author held a Fellowship at the Summer Research Institute of 1952 of the Canadian Mathematical Congress.     

Ratio limit theorems and Tauberian theorems for vector-valued functions and sequences

We prove ratio limit theorems for (C,γ)-means (γ?0) and Abel means of functions and sequences in Banach spaces, and ratio Tauberian theorems for (C,γ)-means (γ?1) and Abel means of functions and sequences in Banach lattices.     

A one-sided Tauberian theorem for the Borel summability method

We establish a quantitative version of Vijayaraghavan's classical result and use it to give a short proof of the known theorem that a real sequence (s_n) which is summable by the Borel method, and which satisfies the one-sided Tauberian condition that is bounded below must be convergent.