Related papers: On the absolute matrix summability factors
We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.
We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
We provide new necessary and sufficient conditions for the convergence of positive series developing Bertran-De Morgan and Cauchy type tests given in [M. Martin, Bull. Amer. Math. Soc. 47(1941), 452-457] and [L. Bourchtein et al, Int. J.…
Let K be an arbitrary field, and a,b,c,d be elements of K such that the polynomials t^2-at-b and t^2-ct-d are split in K[t]. Given a square matrix M with entries in K, we give necessary and sufficient conditions for the existence of two…
In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by…
The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions $f\in$ Lip1 class provides absolute convergence of Fourier series. In particular we found…
Let $x_1,...,x_n$ be a list of real numbers, let $s :=\sum_{i=1}^{n}x_i$ and let $h:\mathbb{N} \rightarrow \mathbb{R}$ be a function. We gave a necessary and sufficient condition for $s>h(n)$ (respectively, $s<h(n)$). Let $G=(V,E)$ be a…
We define a general notion of "summability" of a set $I\subseteq\mathbb{C^{N}}$ and show that some trivial condition necessary for a set to be summable, is also sufficient. We deduce some intresting corollaries.
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of $L^p$ integrability of the function and its…
The paper provides a necessary and sufficient condition for the composition of multivariable formal power series and present the Generalized Chain Rule for formal power series of multiple variables.
In this paper, which is a follow-up to [A. Borobia, R. Canogar, F. De Ter\'an, Mediterr. J. Math. 18, 40 (2021)], we provide a necessary and sufficient condition for the matrix equation $X^\top AX=B$ to be consistent when $B$ is symmetric.…
The paper is about an arithmetic problem in $\F_2[x]$. We give \emph{admissible} (necessary) conditions satisfied by a set of odd prime divisors of perfect polynomials over $\F_2$. This allows us to prove a new characterization of…
In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient…
There is proved the sufficiency of several conditions for the removability of singularities of complex-analytic sets in domains of $\mathbb C^n$.
A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…
A sufficient condition for the convergence of a generalized formal power series solution to an algebraic $q$-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power…
We study sums of $k$-potent matrices. We show the conditions by which a complex matrix $A$ can be expressed as a sums of $k$-potent matrices. Also we obtain conditions by which a complex matrix $A$ can be expressed as a sum of finite order…
Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…
In this paper, by using an almost increasing and $\delta$-quasi-monotone sequence, a general theorem on $\phi-{\mid{C},\alpha\mid}_k$ summability factors, which generalizes a result of Bor \cite{3} on ${\phi-\mid{C},1\mid}_k$ summability…
Necessary and sufficient conditions are obtained on the function $M$ such that $\{ M(x,y) e^{i kx}e^{i my}: (k,m)\in \Omega \}$ is complete and minimal in $L^{p}(\mathbb{T}^{2})$ when $\Omega^{c}=\{(0,0)\}$ and $\Omega^{c} =…