Notes on the unconditional convergence of multidimensional functional series.
On double statistical -convergence of fuzzy numbers.
On evaluations of infinite double sums and Tornheim's double series.
On the evaluation of Euler sums.
On Tornheim's double series
On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions
On Witten multiple zeta-functions associated with semisimple Lie algebras I
We define Witten multiple zeta-functions associated with semisimple Lie algebras , of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case , we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations, we prove...
Quotient mean series.
Rate preservation of double sequences under - type transformation.
Remark on a formula of P.H. Jackson
Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields
Solving some problems of advanced analytical nature posed in the SIAM Review. II.
Some integrability theorems for multiple trigonometric series
Several new integrability theorems are proved for multiple cosine or sine series.
Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense.
Sur les conditions de convergence de certaines séries multiples
Tauberian theorems for Cesàro summable double integrals over
Given ⨍ ∈ , denote by s(w,z) its integral over the rectangle [0,w]× [0,z] and by σ(u,v) its (C,1,1) mean, that is, the average value of s(w,z) over [0,u] × [0,v], where u,v,w,z>0. Our permanent assumption is that (*) σ(u,v) → A as u,v → ∞, where A is a finite number. First, we consider real-valued functions ⨍ and give one-sided Tauberian conditions which are necessary and sufficient in order that the convergence (**) s(u,v) → A as u,v → ∞ follow from (*). Corollaries allow these Tauberian conditions...
Tauberian theorems for Cesàro summable double sequences
be a double sequence of real numbers which is summable (C,1,1) to a finite limit. We give necessary and sufficient conditions under which converges in Pringsheim’s sense. These conditions are satisfied if is slowly decreasing in certain senses defined in this paper. Among other things we deduce the following Tauberian theorem of Landau and Hardy type: If is summable (C,1,1) to a finite limit and there exist constants and H such that , and whenever , then converges. We always mean...
The double sequence space
The matrix transformations of double sequence space of .
The fuzzy numbers defined by a modulus