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Search: MSC category 40 ( Sequences, series, summability )

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1. CMB 2014 (vol 58 pp. 188)

Wirths, Karl Joachim
Telescoping Estimates for Smooth Series
We derive telescoping majorants and minorants for some classes of series and give applications of these results.

Keywords:telescoping series, Stietjes constant, Hardy's formula, Stirling's formula
Categories:26D15, 40A25, 97I30

2. CMB 2011 (vol 55 pp. 172)

Rhoades, B. E.
Hausdorff Prime Matrices
In this paper we give the form of every multiplicative Hausdorff prime matrix, thus answering a long-standing open question.

Keywords:Hausdorff prime matrices

3. CMB 2009 (vol 40 pp. 498)

Selvaraj, Chikkanna; Selvaraj, Suguna
Matrix transformations based on Dirichlet convolution
This paper is a study of summability methods that are based on Dirichlet convolution. If $f(n)$ is a function on positive integers and $x$ is a sequence such that $\lim_{n\to \infty} \sum_{k\le n} {1\over k}(f\ast x)(k) =L$, then $x$ is said to be {\it $A_f$-summable\/} to $L$. The necessary and sufficient condition for the matrix $A_f$ to preserve bounded variation of sequences is established. Also, the matrix $A_f$ is investigated as $\ell - \ell$ and $G-G$ mappings. The strength of the $A_f$-matrix is also discussed.

Categories:11A25, 40A05, 40C05, 40D05

4. CMB 2007 (vol 50 pp. 547)

Iakovlev, Serguei
Inverse Laplace Transforms Encountered in Hyperbolic Problems of Non-Stationary Fluid-Structure Interaction
The paper offers a study of the inverse Laplace transforms of the functions $I_n(rs)\{sI_n^{'}(s)\}^{-1}$ where $I_n$ is the modified Bessel function of the first kind and $r$ is a parameter. The present study is a continuation of the author's previous work %[\textit{Canadian Mathematical Bulletin} 45] on the singular behavior of the special case of the functions in question, $r$=1. The general case of $r \in [0,1]$ is addressed, and it is shown that the inverse Laplace transforms for such $r$ exhibit significantly more complex behavior than their predecessors, even though they still only have two different types of points of discontinuity: singularities and finite discontinuities. The functions studied originate from non-stationary fluid-structure interaction, and as such are of interest to researchers working in the area.

Categories:44A10, 44A20, 33C10, 40A30, 74F10, 76Q05

5. CMB 2005 (vol 48 pp. 175)

Borwein, David; Kratz, Werner
Weighted Convolution Operators on $\ell_p$
The main results deal with conditions for the validity of the weighted convolution inequality $\sum_{n\in\mathbb Z}\left|b_n\sum_{k\in\mathbb Z} a_{n-k}x_k\right|^p\le C^p\sum_{k\in\mathbb Z} |x_k|^p$ when $p\ge1$.

Keywords:convolution operators on $\ell_p$
Categories:40G10;, 40E05

6. CMB 2000 (vol 43 pp. 406)

Borwein, David
Weighted Mean Operators on $l_p$
The weighted mean matrix $M_a$ is the triangular matrix $\{a_k/A_n\}$, where $a_n > 0$ and $A_n := a_1 + a_2 + \cdots + a_n$. It is proved that, subject to $n^c a_n$ being eventually monotonic for each constant $c$ and to the existence of $\alpha := \lim \frac{A_n}{na_n}$, $M_a \in B(l_p)$ for $1 < p < \infty$ if and only if $\alpha < p$.

Keywords:weighted means, operators on $l_p$, norm estimates
Categories:47B37, 47A30, 40G05

7. CMB 1999 (vol 42 pp. 184)

Fiorito, Giovanni
On Arithmetic Means of Sequences Generated by a Periodic Function
In this paper we prove the convergence of arithmetic means of sequences generated by a periodic function $\varphi (x) $, moreover if $\varphi (x) $ satisfies a suitable symmetry condition, we prove that their limit is $\varphi (0) $. Applications of previous results are given to study other means of sequences and the behaviour of a class of recursive series.


8. CMB 1998 (vol 41 pp. 10)

Borwein, David
Simple conditions for matrices to be bounded operators on $l_p$
The two theorems proved yield simple yet reasonably general conditions for triangular matrices to be bounded operators on $l_p$. The theorems are applied to N\"orlund and weighted mean matrices.

Keywords:Triangular matrices, Nörlund matrices, weighted means, operators, on $l_p$.
Categories:47B37, 47A30, 40G05

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