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Magomedrasul Magomed-Kasumov

Magomedrasul Magomed-Kasumov

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35
Publications
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30
Citations

Publications

Publications (35)
Preprint
Full-text available
In this work we obtain a necessary and sufficient condition on 𝛼, 𝛽 for Fourier--Jacobi series to be uniformly convergent to absolutely continuous functions.
Article
We establish that the Fourier series in the Sobolev system of polynomials \( {\mathcal{P}}_{r}^{\alpha,\beta} \), with \( -1<\alpha,\beta\leq 0 \), associated to the Jacobi polynomials converge uniformly on \( [-1,1] \) to functions in the Sobolev space \( W^{r}_{L^{1}_{\rho(\alpha,\beta)}} \), where \( \rho(\alpha,\beta) \) is the Jacobi weight. W...
Article
The territory of Dagestan is one of the seismically active regions of the European part of Russia. Both in the historical past and in recent years, strong and destructive earthquakes have occurred in this region. For example, the area of the Sulak cascade of hydroelectric power stations is one of the most dangerous in Dagestan, both in seismic and...
Article
Получено представление систем функций $\Phi_1$, ортогональных относительно скалярного произведения типа Соболева с одной дискретной точкой, в терминах функций систем, ортогональных в $L^2$. Исследованы вопросы полноты системы $\Phi_1$. Изучены некоторые свойства систем функций, полученных дифференцированием системы $\Phi_1$. Библиография: 3 названи...
Article
We consider new conditions for existence and uniqueness of a Caratheodory solution for an initial value problem with a discontinuous right-hand side. The method used here is based on:1) the representation of the solution as a Fourier series in a system of functions orthogonal in Sobolev sense and generated by a classical orthogonal system;2) the us...
Article
We consider the properties of systems of functions \(\Phi_1\) orthogonal with respect to a discrete-continuous Sobolev inner product of the form \(\langle f,g \rangle_S = f(a)g(a)+f(b)g(b)+\int_a^b f'(t)g'(t)dt\). In particular, we study the completeness of systems \(\Phi_1\) in the Sobolev space \(W^1_{L^2}\). Additionally, we analyze the properti...
Article
The work describes the research and development carried out at the DD GS RAS over the past 5 years, mainly of an innovative nature. These developments include the computer program "Con-struction the transfer function between time series based on the relative amplitudes of coherent harmonics", invention "Method for reconstructing dynamic processes i...
Chapter
It is shown that the approximation rate of continuous functions by Vallée Poussin means Vn,mα(f) of special series partial sums (α is a parameter in special series construction) is of the order of the best approximation provided 12
Article
В данной статье рассматриваются алгоритмы и программа прямого и обратного быстрого преобразования Фурье по системе функций, ортогональных по системе Соболева и порожденных системой Уолша.
Article
Разработан алгоритм и компьютерная программа для количественной оценки надежности геохимических предвестников землетрясений, выявленных ранее по визуальному сопоставлению временных рядов. С использованием программы обработаны геохимические временные ряды, полученные на пункте Дубки (водород, 2004-2019 гг.) и на пункте Караман (гелий, 2006-2011 и 20...
Article
Basing on Fourier’s trigonometric sums and the classical de la Vallée-Poussin means, we introduce the repeated de la Vallée-Poussin means. Under study are the approximation properties of the repeated means for piecewise smooth functions. We prove that the repeated means achieve the rate of approximation for the discontinuous piecewise smooth functi...
Article
Properties of functions from the Sobolev orthogonal system \(\mathfrak{W}_{r}\) generated by the Walsh system are studied. In particular, recurrence relations for functions from \(\mathfrak{W}_{1}\) are obtained. The uniform convergence of Fourier series in the system \(\mathfrak{W}_{r}\) to functions f from the S obolev spaces \(W_{{L^p}}^r\), p ≥...
Article
Изучены свойства функций из ортогональной по Соболеву системы $\mathfrak W_r$, порожденной системой Уолша. В частности, получены рекуррентные соотношения для функций из $\mathfrak W_1$. Доказана равномерная сходимость рядов Фурье по системе $\mathfrak W_r$ к функциям $f$ из пространств Соболева $W^r_{L^p}$, $p\ge 1$, $r=1,2,…$ . Библиография: 9 наз...
Article
Full-text available
We obtain exact order-of-magnitude estimates of piecewise smooth functions approximation by trigonometric Fourier sums. It is shown that in continuity points Fourier series of piecewise Lipschitz function converges with rate $\ln n/n$. If function $f$ has a piecewise absolutely continuous derivative then it is proven that in continuity points decay...
Article
The authors continue study of special series with sticking property (r-fold coincidence at points ± 1) in ultraspherical Jacobi polynomials, that was started in the previous works of the first author. In the present paper they are dealing with an approximative properties of Valleé-Poussin means for partial sums of the mentioned special series. It i...
Article
We consider the problem of representing a solution to the Cauchy problem for an ordinary differential equation as a Fourier series in polynomials l r,k α(x) (k = 0, 1,...) that are Sobolev-orthonormal with respect to the inner product $$\left\langle {f,g} \right\rangle = \sum\limits_{v = 0}^{r - 1} {{f^{(v)}}(0){g^{(v)}}} (0) + \int\limits_0^\infty...
Article
The value of the deviation of a function f(x) from its de la Vallée-Poussin means Vmⁿ(f, x) with respect to the trigonometric system for classes of piecewise smooth 2π-periodic functions is estimated.
Article
Full-text available
Linear system in which the input signal y=y(t) and the output x=x(t) are related by the equation x(r)(t)=∑r−1ν=0aν(t)x(ν)(t)+∑sμ=0bμ(t)y(μ)(t) is considered. The goal is to find the unknown variable coefficients aν(t) (ν=0,…,r−1) and bμ(t) (μ=0,…,s) in case when the signal values are given in the nodes of a uniform grid ΩN={tj=−1+jh}N−1j=0, where h...
Article
We obtain an exact description for the behavior of Fourier-Haar sums at dyadic irrational discontinuity points for functions of bounded variation.
Article
It is well known, that hydrogeodynamic observations, including measurement of production output of blowing wells and water level registration in wells with negative level, are one of the most accessible means of Earth crust deformation monitoring, which usually used for seismic forecasting. Practically the most informative of them is observation of...

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