In this paper we construct an integrable function of two variables for which the double Fourier-Walsh series converges both by rectangles and by spheres. Besides, we show that the coefficients of the series on the spectrum are positive and are arranged in decreasing order in all directions. Also, it is proved that after a suitable choice of signs for the Fourier coefficients of the series the spherical

In this paper we prove some strong convergence theorems for partial sums with respect to Vilenkin system.

The main purpose of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of analytic functions, which are defined here by means of a newly defined q-linear differential operator.

A group is called an n-torsion group if it has a system of defining relations of the form rn = 1 for some elements r, and for any of its finite order element a the defining relation an = 1 holds. It is assumed that the group can contain elements of infinite order. In this paper, we show that for every odd n ≥ 665 for each n-torsion group can be constructed a theory similar to that of constructed in

Motivated by the ordinary Gabor frames in L2(ℝd) and operator-valued frames on abstract Hilbert spaces, we investigate operator-valued Gabor frames associated with locally compact Abelian groups. Necessary and sufficient conditions for an operator-valued Gabor frame to admit a Parseval/tight Gabor dual are given. In particular, we consider a special case, which includes the case of ordinary Gabor frames

In this paper, we prove that if {nk} is an arbitrary increasing sequence of natural numbers such that the ratio nk+1/nk is bounded, then the nk-th partial sum of a series by Franklin system cannot converge to +∞ on a set of positive measure. Also, we prove that if the ratio nk+1/nk is unbounded, then there exists a series by Franklin system, the nk-th partial sum of which converges to +∞ almost everywhere

It is known that for a wide class of discrete-time stationary processes possessing spectral densities f, the variance σ2n(f) of the best linear unbiased estimator for the mean depends asymptotically only on the behavior of the spectral density f near the origin, and behaves hyperbolically as n → ∞. In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease

In this paper, we focus on a conjecture concerning uniqueness problem of meromorphic functions sharing three distinct polynomials with their difference operators, which is mentioned in Chen and Yi (Result Math v. 63, pp. 557–565, 2013), and prove that it is true for meromorphic functions of finite order. Also, a result of Zhang and Liao, obtained for entire functions (Sci China Math v. 57, pp. 2143–2152

Different generalized Cesáro summation methods are compared with each other. Analogous of Hardy’s theorem, concerning the order of the partial sums of trigonometric Fourier series, for generalized Cesáro means are obtained.

The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set \(W\subset\mathbb{R}_+^n\) containing the intersection of some neighborhood of the origin with \(\mathbb{R}_+^n\). It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series

The paper is devoted to the solvability questions of the Wiener-Hopf integral equation in the case where the kernel K satisfies the conditions 0 ≤ K ∈ L1(ℝ), \(\int_{-\infty}^{\infty} K(t)dt>1\), K(±x) ∈ C(3)(ℝ+), (−1)nK(±x)(n)(x) ≥ 0, x ∈ ℝ+, n =1, 2, 3. Based on Volterra factorization of the Wiener-Hopf operator, and invoking the technique of nonlinear functional equations, we construct real-valued

In this paper, we study bivariate homogeneous interpolation polynomials. We show that the homogeneous Lagrange interpolation polynomial of a sufficiently smooth function converges to a homogeneous Hermite interpolation polynomial when the interpolation points coalesce.

The present paper is devoted to the study of existence and uniqueness of a solution and Ulam type stabilities for Volterra delay integro-differential equations on a finite interval. Our analysis is based on the Pachpatte’s inequality and Picard operator theory. Examples are provided to illustrate the stability results obtained in the case of a finite interval. Also, we give an example to illustrate

We derived a convergence result for a sequential procedure known as alternating maximization (minimization) to the maximum likelihood estimator for a pretty large family of models - Generalized Linear Models. Alternating procedure for linear regression becomes to the well-known algorithm of Alternating Least Squares, because of the quadraticity of log-likelihood function L(υ). In Generalized Linear

The paper considers some functions depending on the realizations of a random process with log-normal distribution and two types of expectations. The interpretations of these functions and expectations are given in terms of actuarial mathematics. The comparison of the behavior of these two types of expectations is given using the Black-Scholes formulas. Criteria for a random process to obey a stochastic

We define sparse operators of strong type on abstract measure spaces with ball-bases. Weak and strong type inequalities for such operators are proved.

In this paper the concept of interassociativity via hyperidentities of associativity is extended and describe the set of semigroups which are {i, j}-interassociative to the free semigroup and the free commutative semigroup, where i, j = 1, 2, 3.

In 1987 Harris proved-among others that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ Lp such that its triangular Walsh-Fourier series does not converge almost everywhere. In this paper we prove that the set of the functions from the space Lp(II2) (1 ≤ p < 2) with subsequence of triangular partial means \(S_{2^A}^\Delta(f)\) of the double Walsh-Fourier series convergent in measure

Let {X(t), t ∈ ℝ} be a centered real-valued stationary Gaussian process with spectral density f. The paper considers a question concerning asymptotic distribution of tapered Toeplitz type quadratic functional \(Q_T^h\) of the process X(t), generated by an integrable even function g and a taper function h. Sufficient conditions in terms of functions f, g and h ensuring central limit theorems for standard

In this paper, we prove a difference analogue of Cartan’s second main theorem for a meromorphic mapping on ℂm intersecting a finite set of fixed hyperplanes in general position on ℙn(ℂ). As an application, we prove a uniqueness theorem for a class of holomorphic curves by inverse images of n + 4 hyperplanes. This result is so far the best result about the uniqueness problem for holomorphic curves by