Expand all Collapse all | Results 1 - 7 of 7 |
1. CMB 2011 (vol 55 pp. 172)
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 Category:40G05 |
2. CMB 2007 (vol 50 pp. 547)
Inverse Laplace Transforms Encountered in Hyperbolic Problems of Non-Stationary Fluid-Structure Interaction |
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 |
3. CMB 2005 (vol 48 pp. 175)
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 |
4. CMB 2000 (vol 43 pp. 406)
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 |
5. CMB 1999 (vol 42 pp. 184)
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.
Category:40A05 |
6. CMB 1998 (vol 41 pp. 10)
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, NÃ¶rlund matrices, weighted means, operators, on $l_p$. Categories:47B37, 47A30, 40G05 |
7. CMB 1997 (vol 40 pp. 498)
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 |