Distinguished subsets and summability invariants
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel...
Divergent sequences satisfying the linear fractional transformations.
Divergent vector sequences {yₙ} with Δyₙ → 0
An approximation property of divergent sequences in normed vector spaces is discussed.
Dot product rearrangements.
Double sequence core theorems.
Double Sequence Spaces Definedby a Sequence of Modulus Functions over -normed Spaces
In the present paper we introduce some double sequence spaces defined by a sequence of modulus function over -normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces.
Double sequence spaces over -normed spaces
In this paper, we define some classes of double sequences over -normed spaces by means of an Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined.
Double Sequences and Iterated Limits in Regular Space
First, we define in Mizar [5], the Cartesian product of two filters bases and the Cartesian product of two filters. After comparing the product of two Fréchet filters on ℕ (F1) with the Fréchet filter on ℕ × ℕ (F2), we compare limF₁ and limF₂ for all double sequences in a non empty topological space. Endou, Okazaki and Shidama formalized in [14] the “convergence in Pringsheim’s sense” for double sequence of real numbers. We show some basic correspondences between the p-convergence and the filter...
Double Sequences and Limits
Double sequences are important extension of the ordinary notion of a sequence. In this article we formalized three types of limits of double sequences and the theory of these limits.
Double Series and Sums
In this paper the author constructs several properties for double series and its convergence. The notions of convergence of double sequence have already been introduced in our previous paper [18]. In section 1 we introduce double series and their convergence. Then we show the relationship between Pringsheim-type convergence and iterated convergence. In section 2 we study double series having non-negative terms. As a result, we have equality of three type sums of non-negative double sequence. In...
Dual pairs of sequence spaces.
Durch Matrixverschiebungen erweiterte Konvergenzbegriffe.