We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...

We study Tauberian conditions for the existence of Cesàro limits in terms of the Laplace transform. We also analyze Tauberian theorems for the existence of distributional point values in terms of analytic representations. The development of these theorems is parallel to Tauber’s second theorem on the converse of Abel’s theorem. For Schwartz distributions, we obtain extensions of many classical ...

Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...

Klaus Leidorf, Peter Ettel, Walter Irlinger, Joachim Zeune, Burgen in Bayern. 7000 Jahre Geschichte im Luftbild. Mit Beiträgen von Björn-Uwe Abels , Jochen Haberstroh, Dieter Neubauer, Michael M. Rind, Karl-Heinz Röhrig, Stuttgart (Theiss) 1999. 208 S., ca. 300 farbige Abb., 80 Pläne

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion modulus smoothness, we also derive an associated concerning rate convergence these Furthermore, through example, illustrate that our summability- based Korovin has advantage over proved in seminal paper by Anastassiou (Stud. Univ. Babeş...

Abel, Bord, Cesâro, Holder and Hausdorff, Journal d'Analyse Mathématique vol. 3 (1953-1954) pp. 346-381. 2. -, On a converse of Abel's theorem, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 244-256. 3. W. W. Rogosinski, On Hausdorff methods of summability, Proc. Cambridge Philos. Soc. vol. 38 (1942) pp. 166-192. 4. O. Szász, On the product of two summability methods, Annales de la Société Polonaise ...

3 General results on summability and duality 4 3.1 Total algebras and duality . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Series and infinite sums . . . . . . . . . . . . . . . . . . . 4 3.1.2 Summable families in Hom spaces. . . . . . . . . . . . . . 5 3.1.3 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Theorem of Cartier-Quillen-Milnor-Moore (analytic form) . ....

0. Preface. This article is a survey of certain aspects of the theory of multiple Fourier and trigonometric series. I t is by no means meant to be a complete survey; for example, it is practically disjoint with the material covered on the subject in Zygmund's book [38, Chapter 17.]. There are eight sections to this survey. §1 is the introduction. §2, §3, and §4 are expository in the sense that ...

A weighted mean matrix, denoted by (N , pn), is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn := ∑n k=0 pk. Mishra and Srivastava [1] obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix (N , pn). Bor [2] extended this result to absolute sum...