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Convergence of General Fourier Series of Differentiable Functions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 V. Tsagareishvili
Abstract Convergence of classical Fourier series (trigonometric, Haar, Walsh, \(\dots\) systems) of differentiable functions are trivial problems and they are well known. But general Fourier series, as it is known, even for the function \(f(x)=1\) does not converge. In such a case, if we want differentiable functions with respect to the general orthonormal system (ONS) \((\varphi_{n})\) to have convergent
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Derivatives of Meromorphic Functions Sharing Polynomials with Their Difference Operators J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 M.-H. Wang, J.-F. Chen
Abstract In this paper, we investigate the uniqueness of meromorphic functions of finite order \(f(z)\) concerning their difference operators \(\Delta_{c}f(z)\) and derivatives \(f^{\prime}(z)\) and prove that if \(\Delta_{c}f(z)\) and \(f^{\prime}(z)\) share \(a(z)\), \(b(z)\), \(\infty\) CM, where \(a(z)\) and \(b(z)\) are two distinct polynomials, then they assume one of following cases: \((1)\)
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On Khinchin’s Theorem about the Special Role of the Gaussian Distribution J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 L. A. Khachatryan
Abstract The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform integrability of the squares of normed sums of random variables and, thus, the passage to the limit under the expectation sign. The latter provides a simple proof
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Crossing Malmquist Systems with Certain Types J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 F. N. Wang, K. Liu
Abstract In this paper, we will present the expression of meromorphic solutions on the crossing differential or difference Malmquist systems of certain types using Nevanlinna theory. For instance, we consider the admissible meromorphic solutions of the crossing differential Malmquist system$$\begin{cases}f^{\prime}_{1}(z)=\frac{a_{1}(z)f_{2}(z)+a_{0}(z)}{f_{2}(z)+d_{1}(z)},\\ f^{\prime}_{2}(z)=\fr
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Entire Functions and Their High Order Difference Operators J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 S. Majumder, N. Sarkar, D. Pramanik
Abstract In this paper, we prove that for a transcendental entire function \(f\) of finite order such that \(\lambda(f-a)<\rho(f)\), where \(a\) is an entire function and satisfies \(\rho(a)<\rho(f)\), \(n\in\mathbb{N}\), if \(\Delta_{c}^{n}f\) and \(f\) share the entire function \(b\) satisfying \(\rho(b)<\rho(f)\) CM, where \(c\in\mathbb{C}\) satisfies \(\Delta_{c}^{n}f\not\equiv 0\), then \(f(z)=a(z)+de^{cz}\)
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Simple Proof of the Risk Bound for Denoising by Exponential Weights for Asymmetric Noise Distributions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 A. S. Dalalyan
Abstract In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this result was already known for a wide class of symmetric noise distributions, the extension to asymmetric distributions presented in this note is new.
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Orientation-Dependent Chord Length Distribution in a Convex Quadrilateral J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-12-28 D. M. Martirosyan
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Operator Preserving Bernstein-Type Inequalities between Polynomials J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 A. Mir, A. Hussain
Abstract In this paper, we establish some operator preserving inequalities of Bernstein-type in the uniform-norm between univariate complex coefficient polynomials while taking into account the placement of their zeros. The obtained results produce a variety of interesting results as special cases.
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On a Generalization of an Operator Preserving Turán-Type Inequality for Complex Polynomials J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 S. A. Malik, B. A. Zargar
Abstract Let \(W(\zeta)=(a_{0}+a_{1}\zeta+...+a_{n}\zeta^{n})\) be a polynomial of degree \(n\) having all its zeros in \(\mathbb{T}_{k}\cup\mathbb{E}^{-}_{k}\), \(k\geq 1\), then for every real or complex number \(\alpha\) with \(|\alpha|\geq 1+k+k^{n}\), Govil and McTume [7] showed that the following inequality holds $$\max\limits_{\zeta\in\mathbb{T}_{1}}|D_{\alpha}W(\zeta)|\geq n\left(\frac{|\a
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Comparison of Polynomials and Weighted-Hyperbolic Operators J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 M. A. Khachaturyan, V. N. Margaryan
Abstract In the language of zero multiplicities of subpolynomials, the sufficient conditions are found under which a polynomial of two variables is hyperbolic with a given weight when its leading part is Gårding hyperbolic.
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Effectiveness of the Even-Type Delayed Mean in Approximation of Conjugate Functions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 Xh. Z. Krasniqi
Abstract In this paper, using the even-type delayed mean of conjugate series, we have obtain the degree of approximation for a conjugate function in the metric of the generalized Höder class with weight. Involving two moduli of continuity, we have shown that the even-type delayed mean are streamlined to guarantee this degree to be of the Jackson order.
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A Hardy–Littlewood Type Theorem for Harmonic Bergman–Orlicz Spaces and Applications J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 Xi Fu, Q. Shi#
Abstract It is well known that a harmonic function is in a Bergman space if and only if it satisfies some Hardy–Littlewood type integral estimates. In this paper, we extend this result to harmonic Bergman–Orlicz spaces. As an application, Lipschitz-type characterizes of harmonic Bergman–Orlicz spaces on the unit ball with respect to pseudo-hyperbolic, hyperbolic and Euclidean metrics are established
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Erratum to: Some Results on Nonlinear Difference-Differential Equations J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 L. L. Wu, M. L. Liu#, P. C. Hu
An Erratum to this paper has been published: https://doi.org/10.3103/S1068362323300015
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Distribution of Zeros and Critical Points of a Polynomial, and Sendov’s Conjecture J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 G. M. Sofi, W. M. Shah
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Further Results on Shared-Value Properties of $$\boldsymbol{f^{\prime}(z)=f(z+c)}$$ J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 M. Qiu, X. Qi
Abstract In this paper, we will continue to consider ‘‘under what sharing value conditions, does \(f^{\prime}(z)=f(z+c)\) hold?’’ For example, we prove the following result: Let \(f(z)\) be a meromorphic function of hyper-order strictly less than 1, and let \(a,b\) be two distinct constants. If \(f^{\prime}(z)\) and \(f(z+c)\) share \(\infty\) CM and \(a\), \(b\) IM, and if \(N(r,f)=O(\overline{N}(r
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On the Uniform Convergence of Spherical Partial Sums of Fourier Series by the Double Walsh System J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-10-19 S. A. Sargsyan, L. N. Galoyan
Abstract In this paper, we construct a two-variable integrable function \(U\) whose Fourier coefficients by the double Walsh system are positive on the spectrum and arranged in decreasing order in all directions. For each almost everywhere finite measurable function \(f(x,y)\), \((x,y)\in[0,1)^{2}\), and for any \(\delta>0\) it is possible to find a bounded function \(g(x,y)\) such that $$|\{(x,y)\in[0
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On the Uniqueness of L-functions and Meromorphic Functions Sharing a Set J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 S. Mallick, D. Sarkar
Abstract The paper presents general criterions for the uniqueness of a nonconstant meromorphic function having finitely many poles and a nonconstant L-function in the Selberg class when they share a set. Our results significantly improve all the existing results in this direction [4, 16, 17, 22] with extent to the most general setting. As a consequence, we have incorporated a large number of examples
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Existence and Stability of Integro Differential Equation with Generalized Proportional Fractional Derivative J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 S. Harikrishnan, D. Vivek, E. M. Elsayed
Abstract In this study, integro-differential equations of arbitrary order are studied. The fractional order is expressed in terms of the \(\psi\)-Hilfer type proportional fractional operator. This research exposes the dynamical behavior of integro-differential equations with fractional order, such as existence, uniqueness, and stability solutions. The initial value problem and nonlocal conditions are
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On the Issue of Convergence and Summability of General Fourier Series J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 L. Gogoladze, G. Tsagareishvili
Abstract The paper considers the issues of convergence and summability of Fourier series of the functions of class \(\textrm{Lip}1\) for general orthonormal systems (GOSs). The sufficient conditions for the GOS functions are found that make the Fourier series in this system of each function from the class \(\textrm{Lip}1\) converging almost everywhere, unconditionally converging, or being summable
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Operators on Mixed-Norm Amalgam Spaces via Extrapolation J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 Y. Lu, J. Zhou#, S. Wang
Abstract Let \(t\in(0,\infty)\), \(\vec{p}\in(1,\infty)^{n}\) and \(\vec{q}\in[1,\infty)^{n}\). We establish versions of the Rubio de Francia extrapolation theorem, and further obtain the bounds for some classical operators and the commutators in harmonic analysis on the mixed-norm amalgam space \((L^{\vec{p}},L^{\vec{q}})_{t}({\mathbb{R}^{n}})\). As an application, a characterization of the mixed-norm
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$$\boldsymbol{(P,Q)}$$ – $${\varepsilon}$$ -Pseudo Condition Spectrum for $$\mathbf{2\times 2}$$ Matrices. Linear Operator and Application J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 J. Banaś, A. B. Ali, K. Mahfoudhi, B. Saadaoui
Abstract We define a new type of spectrum, called the \((P,Q)\)–\(\varepsilon\)-pseudo condition spectra $$\Sigma_{(P,Q)-\varepsilon}^{(2)}(T)=\sigma_{(P,Q)}^{(2)}(T)\bigcup\left\{\lambda\in\mathbb{C}:||(\lambda-T)_{(P,Q)}^{(2)}||\ ||\lambda-T||>\displaystyle{\frac{1}{\varepsilon}}\right\}.$$ This \((P,Q)\)–\(\varepsilon\)-pseudo condition spectrum shares some properties of the usual spectrum such
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Generalizations of Some Differential Inequalities for Polynomials J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 M. Y. Mir, S. L. Wali, W. M. Shah
Abstract We consider polynomials of the form \(P(z)=z^{s}\big{(}a_{0}+\sum_{v=t}^{n-s}a_{v}z^{v}\big{)},\ t\geq 1,\ 0\leq s\leq n-1\) and prove some results for the estimate of the polar derivative \(D_{\alpha}P(z):=nP(z)+(\alpha-z)P^{\prime}(z)\) and generalize the results due to Aziz and Shah [4], Govil [12] and others.
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Some Results on Nonlinear Difference-Differential Equations J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-08-22 L. L. Wu, M. L. Liu, P. C. Hu
Abstract We describe transcendental entire solutions of certain nonlinear difference-differential equations of the forms: $$f(z)^{2}+f(z)[af^{\prime}(z)+bf(z+c)]+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}$$ and $$f(z)^{n}+f(z)^{n-1}[af^{\prime}(z)+bf(z+c)]+q(z)e^{Q(z)}f(z+c)=p_{1}e^{\lambda_{1}z}+p_{2}e^{\lambda_{2}z},$$ where \(q(z)\), \(Q(z)\), \(u(z)\), \(v(z)\) are nonzero polynomials, \(a\), \(b\), \(c\)
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A Note on Lagrange Interpolation at Principal Lattices J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 Nguyen Van Minh
Abstract We give a geometric condition on principal lattices in \(\mathbb{R}^{n}\) that ensures that the corresponding Lagrange interpolation polynomials of any sufficient smooth function converges to a Taylor polynomial.
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Extremal Problems for a Polynomial and Its Polar Derivative J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 Abdullah Mir
Abstract This paper considers the well known Erdős–Lax and Turán-type inequalities that relate the uniform norm of a univariate complex coefficient polynomial to that of its derivative on the unit circle in the plane. Here, we establish some new inequalities that relate the uniform norm of a polynomial and its polar derivative while taking into account the placement of the zeros and the extremal coefficients
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Weighted Norm Inequalities for Calderón–Zygmund Operators of $$\phi$$ -Type and Their Commutators J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 Li Hang, Jiang Zhou
Abstract In this paper, we introduce new weighted Morrey spaces \(L^{p,\kappa}_{\theta,\omega}(\phi)\) associated with a nondecreasing function \(\phi\) of upper type \(\beta\) with \(\beta>0\), where \(\omega\in A^{\theta}_{p}(\phi)\) and \(\phi(\alpha t)\leqslant C\alpha^{\beta}\phi(t)\), then we obtain the weighted strong type and weak endpoint estimates for Calderón–Zygmund operators of \(\phi\)-type
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On Uniqueness of Meromorphic Solutions to Delay Differential Equation J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 Yishuo Du, Jilong Zhang
Abstract In this paper, we investigate uniqueness of finite-order transcendental meromorphic solutions of the following two equations: $$f(z+1)-f(z-1)+a(z)\frac{f^{\prime}(z)}{f(z)}=R(z,f)=\frac{\sum_{m=0}^{3}a_{m}f^{m}(z)}{\sum_{n=0}^{2}b_{n}f^{n}(z)},$$ and $$f(z+1)f(z-1)+a(z)\frac{f^{\prime}(z)}{f(z)}=R(z,f)=\frac{\sum_{m=0}^{4}a_{m}f^{m}(z)}{\sum_{n=0}^{3}b_{n}f^{n}(z)},$$ where \(R(z,f)\) is an
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Knots of Plane Curves. Applications to ODE J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 G. Barsegian
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Hellinger’s Distance and Correlation for a Subclass of Stable Distributions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 M. T. Mesropyan, V. G. Bardakhchyan
Abstract We investigated correlation retrieval procedure from Hellinger’s distance. We found monotone relation of Hellinger’s distance and positive correlation in a subclass of stable distributed random variables, with \(\alpha>1\) and \(\mu=\beta=0\). We implemented a technique suitable for the class of stable distributions, and showed that this positive relation holds even for the case of Levy distribution
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Weakly Consistent Offline Clustering of ARMA Processes J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 G. L. Adamyan
Abstract In this paper, we consider the problem of weakly consistent offline clustering of ARMA processes. Under the provided assumptions we derive a weakly consistent clustering algorithm of invertible ARMA processes according to their forecast functions. Using BIC penalized quasi-maximum likelihood estimate of the distance function the weak consistency of Algorithm 1 is proven when the target number
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An Application of Ricceri Theorem in Solving Boundary Value Problems J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 S. Shokooh
Abstract Professor Ricceri very recently in the interesting paper has obtained a global minima theorem. In this paper, we will provide an application of this theorem.
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A Schrödinger–Poisson System with the Critical Growth on the First Heisenberg Group J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-06-28 Zhenyu Guo, Qingying Shi
Abstract In this paper, we study the Schrödinger–Poisson system with the critical growth on the first Heisenberg group. With the aid of the Green’s representation formula, the concentratio-compactness and the critical point theory, the existence of ground state solution.
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Some Best Proximity Point Results in the Orthogonal $$0$$ -Complete $$b$$ -Metric-Like Spaces J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 M. Gardašević-Filipović, K. Kukić, D. Gardašević, Z. D. Mitrović
Abstract Since Gordji et al. [26] suggested the concept of the orthogonal set, many authors investigated a uniqueness of best proximal point, but they used continuity of metric \(d\). Here, we proved the uniqueness of the best proximal point under Banach and Hardy–Rodgers type of contraction with appropriate conditions in the orthogonal \(0\)-complete \(b\)-metric-like spaces without continuity conditions
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Investigation of Convex Bodies in $${\mathbf{R}}^{\mathbf{3}}$$ by Support Planes J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 H. O. Harutyunyan, V. K. Ohanyan
Abstract Let \({\mathbf{R}}^{3}\) be the \(3\)-dimensional Euclidean space and \({\mathbf{D}}\) be a bounded convex body \(D\subset\mathbf{R}^{3}\). Consider a family of support planes for which \({\mathbf{D}}\) is an envelope. How can we obtain information about \(D\) from the support planes? Conditions under which a given convex body is the envelope of a family of planes are obtained. Therefore the
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On the Transfinite Diameters of Related Sets. An Extension of Robinson’s Theorem J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 N. M. Babayan, M. S. Ginovyan
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Menshov-Type Theorem for Divergence Sets of Sequences of Localized Operators J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 M. G. Grigoryan, A. Kamont, A. A. Maranjyan
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Uniqueness of Series by General Franklin System with Convergent Subsequence of Partial Sums J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 G. G. Gevorkyan, V. G. Mikaelyan
Abstract The paper considers the series by general Franklin system generated by strongly regular partitioning of the segment \([0,1]\). For such series, with coefficients satisfying a certain necessary condition, the uniqueness theorems are proved in the case when some subsequence of partial sums of this series converges in measure to a bounded function.
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Schauffler-Type Theorems J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 Yu. M. Movsisyan, D. N. Harutyunyan
Abstract In this work the Belousov theorem on linearity of invertible algebras with the Schauffler \(\forall\exists(\forall)\)-identity is extended to regular division algebras for other associative \(\forall\exists(\forall)\)-identities. For the formulas at consideration, the Schauffler-type theorems are also proved. The results are applicable in cryptography (cf. [1–3]).
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Riesz Multiresolution Analysis on Locally Compact Abelian Groups: Construction and Exceptions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-05-04 Satyapriya, Raj Kumar, F. A. Shah
Abstract In this article, we construct a Riesz multiresolution analysis (MRA) on locally compact Abelian groups (LCA) starting from a suitably given scaling function. Subsequently, we investigate all the conditions under which a scaling function generates a Riesz MRA for \(L^{2}(G)\). Besides, all the results are braced with illustrative examples. Towards the culmination, several exceptions are discussed
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Uniqueness of Meromorphic Functions when Its Shift and First Derivative Share Three Values J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-04-13 R. Mandal, R. Biswas
Abstract This paper brings out some improvements as well as generalization results of a paper of Qi and Yang [17] [Comput. Methods Funct. Theory 20, 159–178 (2020)], which deals with the uniqueness results of \(f^{\prime}(z)\) and \(f(z+c)\). To be more realistic about the obtained results, we exhibit some examples.
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Periodic Orthonormal Spline Systems with Arbitrary Knots as Bases in $$\boldsymbol{H}^{\mathbf{1}}\boldsymbol{(\mathbb{T})}$$ J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-04-13 L. Hakobyan, K. Keryan
Abstract We give a simple geometric characterization of sequences of knots for which the corresponding periodic orthonormal spline system of order \(k\) is a basis in the atomic Hardy space on the torus \(\mathbb{T}\).
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Uniqueness of a Meromorphic Function Partially and Normally Sharing Small Functions with Its Different Variants of Generalized Operator J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-04-13 A. Roy, A. Banerjee
Abstract First of all, in continuation of our previous result related to ‘‘\(2\) CM+\(1\) IM’’ small functions sharing of a meromorphic function of restricted hyper order and its linear shift delay differential operator, in some extend we have been able to answer a question paused by us in [Rendiconti del Circolo Mat. di Palermo, 2021 (Published online)]. As another attempt we improve and extend a
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The Best Uniform Approximations at Angles by Entire Functions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-04-13 S. A. Aleksanyan
Abstract The problem about the best uniform approximation at angle by entire functions is investigated. The new results on uniform approximation are a refinement of the earlier known results. Here, the positive answer is provided to the problem proposed by Kober: Suppose that a function \(f\) is holomorphic inside \(\Delta_{\alpha}\), continuous and bounded on \(\Delta_{\alpha}\) for \(\alpha\in\left(0
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On the Gasca–Maeztu Conjecture for $$\boldsymbol{n=6}$$ J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2023-04-13 H. Hakopian, G. Vardanyan, N. Vardanyan
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Geometric Properties of Normalized Le Roy-Type Mittag-Leffler Functions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-12-23 K. Mehrez, D. Bansal
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Some Problems of Convergence of General Fourier Series J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-12-23 V. Tsagareishvili, G. Tutberidze
Abstract Banach [1] proved that good differential properties of function do not guarantee the a.e. convergence of the Fourier series of this function with respect to general orthonormal systems (ONS). On the other hand it is very well known that a sufficient condition for the a.e. convergence of an orthonormal series is given by the Menshov–Rademacher Theorem. The paper deals with sequence of positive
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Meromorphic Functions Sharing Three Values with Their Derivatives in an Angular Domain J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-12-23 B. Pan, W. C. Lin
Abstract In this paper, we investigate the uniqueness of transcendental meromorphic functions sharing three values with their derivatives in an arbitrary small angular domain including a Borel direction. The results extend the corresponding results from Gundersen, Mues and Steinmetz, Zheng, Li et al., and Chen.
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On the $$L^{p}$$ -Greedy Universal Functions with Respect to the Generalized Walsh System J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-12-23 S. A. Episkoposyan, T. M. Grigoryan, L. S. Simonyan
Abstract In this work the function \(U\in L^{1}[0,1)\) is constructed that possesses greedy universality with respect to the generalized Walsh system.
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On a Riemann Boundary Value Problem in the Space of $$\boldsymbol{p}$$ -Summable Functions with Infinite Index J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-12-23 S. Aghekyan
Abstract The paper considers the Riemann boundary value problem in the half-plane in the space \(L^{p}(\rho)\), where weight function \(\rho(x)\) has infinite number of zeros. A necessary and sufficient condition is obtained for the normal solvability and Noetherianness of the considered problem. If the problem is solvable, solutions are represented in an explicit form.
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Some Estimates for Riesz Transforms Associated with Schrödinger Operators J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-12-23 Y. H. Wang
Abstract Let \(\mathcal{L}=-\Delta+V\) be the Schrödinger operator on \(\mathbb{R}^{n},\) where \(n\geq 3,\) and nonnegative potential \(V\) belongs to the reverse Hölder class \(RH_{q}\) with \(n/2\leq q
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On Comparison of Power of Partially Hypoelliptic Polynomials J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 V. N. Margaryan, H. G. Ghazaryan
Abstract The operators (polynomials) partially hypoelliptic by Gårding, Malgrange, and Ehrenpreis and partially hypoelliptic by Burenkov are compared. The conditions under which the addition of minor terms to a partially hypoelliptic operator of the given type does not violate the type of its partial hypoellipticity are established.
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Multiple Factorization of Skew-Symmetric Matrices J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 B. N. Yengibaryan, N. B. Yengibaryan
Abstract Multiple factorization \(A=\Pi D\Pi^{\textrm{T}}\) is proposed for real skew-symmetric matrix \(A\neq 0\) of order \(n\geq 3\). The block-diagonal factor \(D\) contains skew-symmetric invertible blocks of order 2 and the zero block of order \(n-\textrm{rank}A\) if \(\textrm{rank}A
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On the Nonlinear Factorization Equation in a Normed Ring J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 N. B. Yengibaryan
Abstract A general form of nonlinear factorization equations in rings and normed rings is considered. Using nonlinear factorization equation, two basic facts on the existence of factorization are obtained that were hard to deduce or completely out of reach for the methods of direct construction of inverse factorization. The first of these facts relates to the factorization of near-identity elements
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On Volterra and Wiener–Hopf Integral Operators and Corresponding Equations of the First Kind J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 L. G. Arabadzhyan
Abstract The paper studies the possibility of decomposition of the Wiener–Hopf integral operator \(\mathcal{K}\) in the form \(\mathcal{K}=(\mathcal{I}-\mathcal{V}_{-})\cdot\mathcal{V}_{+}\), where \(\mathcal{I}\) is the identity operator and \(\mathcal{V}_{\pm}\) are the Volterra operators of the form \((\mathcal{V}_{+}f)(x)=\int_{0}^{x}V_{+}(x-t)\,f(t)\,dt\), \((\mathcal{V}_{-}f)(x)=\int_{x}^{\infty}V_{-}(t-x)\
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On Summable Solutions to Two-Dimensional Volterra Integral Equations with Monotone Nonlinearity on a Quarter of the Plane J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 Kh. A. Khachatryan, H. S. Petrosyan
Abstract In this note, the class of two-dimensional Volterra integral equations with monotone nonlinearity on a quarter of the plane is studied. Such equations are met in the dynamic theory of \(p\)-adic strings. The constructive theorem about the existence of a positive summable and bounded solution is proved. The asymptotic behavior of the solution at infinity is investigated. Special examples of
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On the Construction of General Solution to an Unstable System of Differential Equations J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 M. G. Muradyan
Abstract The paper proposes an approach to constructing the general solution of a \(2n\)-dimensional system of differential equations with constant coefficients whose fundamental system consists of \(n\) bounded and \(n\) unbounded solutions as \(t\to+\infty\). The algorithm is based on preliminary solution of two matrix algebraic Riccati equations and stable linear Cauchy problems. The method is implemented
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A System of Integral Equations on the Entire Axis with Convex and Monotone Nonlinearity J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-10-25 A. Kh. Khachatryan, Kh. A. Khachatryan
Abstract A system of nonlinear convolution-type integral equations on the entire axis is considered in this work. This system is met in many areas of mathematical physics and mathematical biology. The issues of existence and absence of nontrivial bounded solutions are investigated. The theorem about the uniqueness of the solution in a certain class of bounded functions is proved. In the end of the
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Infinitely Many Solutions for Kirchhoff-Type Equations Involving Degenerate Operator J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-08-02 J. Chen, L. Li, Sh. Chen
Abstract In this paper, we study the existence of infinitely many nontrivial solutions for a class of nonlinear Kirchhoff-type equation $$-\left(a+b\int\limits_{\mathbb{R}^{N}}|\nabla_{\lambda}u|^{2}dx\right)\Delta_{\lambda}u+V(x)u=f(x,u),\quad\text{in }\mathbb{R}^{N}$$ where constants \(a>0,\ b>0\), \(\Delta_{\lambda}\) is a strongly degenerate elliptic operator, and \(f\) is a function with a more
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The Walsh–Fourier Transform on the Real Line J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-08-02 G. Gát, U. Goginava
Abstract The element of the Walsh system, that is the Walsh functions map from the unit interval to the set \(\{-1,1\}\). They can be extended to the set of nonnegative reals, but not to the whole real line. The aim of this article is to give a Walsh-like orthonormal and complete function system which can be extended on the real line.
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On Fourier Series Almost Universal in the Class of Measurable Functions J. Contemp. Mathemat. Anal. (IF 0.3) Pub Date : 2022-08-02 M. G. Grigoryan
Abstract In this work, a universal trigonometric series is constructed such that, after multiplying the terms of this series by some sequence of signs \(\{\delta_{k}=\pm 1\}_{k=0}^{\infty}\), it can be transformed into the Fourier series of some integrable function.