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On the Weyl Multipliers for General Haar and Franklin Systems 论一般哈尔和富兰克林系统的韦尔乘数
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s106836232470016x
G. Gevorkyan
{"title":"On the Weyl Multipliers for General Haar and Franklin Systems","authors":"G. Gevorkyan","doi":"10.3103/s106836232470016x","DOIUrl":"https://doi.org/10.3103/s106836232470016x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the work the almost everywhere (a.e.) convergence (absolute convergence) of series by the general Haar and Franklin systems corresponding to weakly regular division of the segment <span>([0,1])</span> are compared. It is proved that if a series by the general Haar system diverges (absolutely diverges) on a set <span>(E)</span>, then the series by the general Franklin system with the same coefficients diverges (absolutely diverges) a.e. in <span>(E)</span>. As a consequence, it is obtained that if a sequence <span>(omega_{n})</span> is not a Weyl multiplier for unconditional a.e. convergence of series by the general Haar system, then it is not a Weyl multiplier for unconditional a.e. convergence of series by the general Franklin series.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Erdös–Lax-Type Inequalities for Polynomials 论多项式的厄尔多斯-拉克斯型不等式
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s1068362324700195
I. Nazir, I. A. Wani
{"title":"On the Erdös–Lax-Type Inequalities for Polynomials","authors":"I. Nazir, I. A. Wani","doi":"10.3103/s1068362324700195","DOIUrl":"https://doi.org/10.3103/s1068362324700195","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Erdös–Lax inequality relates the sup norm of the derivative of a polynomial along the unit circle to that of the polynomial itself (on the unit circle). This paper aims to extend the classical Erdös–Lax inequality to the polar derivative of a polynomial by using the extreme coefficients of the given polynomial. The obtained results not only enrich the realm of Erdös–Lax-type inequalities but also offer a promising avenue for diverse applications where these inequalities play a pivotal role. To illustrate the practical significance of our results, we present a numerical example. It vividly demonstrates that our bounds are considerably sharper than the existing ones in the extensive literature on this captivating subject.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classification of Dual Distributive Hyperidentities in Divisible Algebras 可分代数中双重分配超同性的分类
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s1068362324700225
Yu. M. Movsisyan, S. S. Davidov
{"title":"Classification of Dual Distributive Hyperidentities in Divisible Algebras","authors":"Yu. M. Movsisyan, S. S. Davidov","doi":"10.3103/s1068362324700225","DOIUrl":"https://doi.org/10.3103/s1068362324700225","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper provides a classification of nontrivial dual hyperidentities of the left and right distributivity satisfied in functionally nontrivial divisible algebras. If the nontrivial dual hyperidentities of the left and right distributivity hold in a functionally nontrivial divisible algebra, then the hyperidentity of the left distributivity is of rank two and is (equivalent to the hyperidentity) of the form</p><span>$$X(x,Y(y,z))=Y(X(x,y),X(x,z)),$$</span><p>while the hyperidentity of the right distributivity is the hyperidentity of rank two and is (equivalent to the hyperidentity) of the form</p><span>$$X(Y(x,y),z)=Y(X(x,z),X(y,z)).$$</span><p>For the classification of nontrivial hyperidentities of the left and right distributivity satisfying in functionally nontrivial <span>(q)</span>-algebras, see [1–4].</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Solvability of One Infinite System of Integral Equations with Power Nonlinearity on the Semi-Axis 论半轴上幂非线性无穷积分方程组的可解性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s1068362324700201
Kh. A. Khachatryan, H. S. Petrosyan
{"title":"On the Solvability of One Infinite System of Integral Equations with Power Nonlinearity on the Semi-Axis","authors":"Kh. A. Khachatryan, H. S. Petrosyan","doi":"10.3103/s1068362324700201","DOIUrl":"https://doi.org/10.3103/s1068362324700201","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An infinite system of integral equations with power nonlinearity on the positive half-line is considered. A number of particular cases of this system arise in many branches of mathematical physics. In particular, systems of this nature are encountered in the theory of radiative transfer in spectral lines, in the dynamic theory of <span>(p)</span>-adic open-closed strings, in the mathematical theory of the spread of epidemic diseases, and in econometrics. The existence of a nonnegative (in coordinates) nontrivial and bounded solution is proved. Under an additional constraint on the matrix kernel, we also study the asymptotic behavior at infinity. In the case of strong symmetry (symmetry both in coordinates and in indices) of the matrix kernel, we also prove a uniqueness theorem for a solution in a certain class of infinite and bounded vector functions. At the end, concrete examples of an infinite matrix kernel are given that are of practical interest in the above applications.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unconditionality of Periodic Orthonormal Spline Systems in $$boldsymbol{H}^{mathbf{1}}{(mathbb{T})}$$ : Necessity $$boldsymbol{H}^{mathbf{1}}{(mathbb{T})}$$ 中周期正交样条系统的非条件性：必然性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s1068362324700183
L. Hakobyan
{"title":"Unconditionality of Periodic Orthonormal Spline Systems in $$boldsymbol{H}^{mathbf{1}}{(mathbb{T})}$$ : Necessity","authors":"L. Hakobyan","doi":"10.3103/s1068362324700183","DOIUrl":"https://doi.org/10.3103/s1068362324700183","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We give a geometric characterization of knot sequences <span>((s_{n}))</span>, which is a necessary condition for the corresponding periodic orthonormal spline system of arbitrary order <span>(k)</span>, <span>(kinmathbb{N})</span>, to be an unconditional basis in the atomic Hardy space on the torus <span>(H^{1}(mathbb{T}))</span>.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Coefficient Results on the Inverse of Silverman Starlike Functions 西尔弗曼星状函数逆的锐系数结果
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s1068362324700213
L. Shi, M. Arif
{"title":"Sharp Coefficient Results on the Inverse of Silverman Starlike Functions","authors":"L. Shi, M. Arif","doi":"10.3103/s1068362324700213","DOIUrl":"https://doi.org/10.3103/s1068362324700213","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the present paper, we consider a subclass of starlike functions <span>(mathcal{G}_{mu})</span> introduced by Silverman. It is defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the sharp bounds of coefficient problems for the inverse of functions in this class. We derive the upper bounds of some initial coefficients, the Fekete–Szegö type inequality and the second Hankel determinant <span>(mathcal{H}_{2,2}left(f^{-1}right))</span> for <span>(finmathcal{G}_{mu})</span>. On the third Hankel determinant <span>(mathcal{H}_{3,1}left(f^{-1}right))</span>, we give a bound on the inverse of <span>(finmathcal{G})</span>. All the results are proved to be sharp.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Convergence and Summability of Orthogonal Series 论正交序列的收敛性和可求和性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-08-09 DOI: 10.3103/s1068362324700171
L. Gogoladze
{"title":"On the Convergence and Summability of Orthogonal Series","authors":"L. Gogoladze","doi":"10.3103/s1068362324700171","DOIUrl":"https://doi.org/10.3103/s1068362324700171","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the paper, the sufficient conditions are found for the convergence, summability by the Cesàro methods and unconditional convergence almost everywhere of orthogonal series, which are equivalent to the well-known theorems of Menshov–Redemacher, Menshov, and Orlich.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation by Haar and Walsh Polynomials in Weighted Generalized Grand Lebesgue Space 加权广义大勒贝格空间中的哈尔多项式和沃尔什多项式逼近法
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-07-09 DOI: 10.3103/s1068362324700079
B. I. Golubov, S. S. Volosivets
{"title":"Approximation by Haar and Walsh Polynomials in Weighted Generalized Grand Lebesgue Space","authors":"B. I. Golubov, S. S. Volosivets","doi":"10.3103/s1068362324700079","DOIUrl":"https://doi.org/10.3103/s1068362324700079","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the paper we give direct theorems on approximation by Haar and Walsh polynomials in weighted generalized grand Lebesgue space. Also the degree of approximation by Borel, Euler, Riesz–Zygmund, and Nörlund linear means of Walsh–Paley–Fourier series are treated in the above cited space.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Meromorphic Solutions for the Fermat-Type Differential-Difference Equations 费马微分方程的非定常解
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-07-09 DOI: 10.3103/s1068362324700122
X. Zhu, X. Qi
{"title":"Meromorphic Solutions for the Fermat-Type Differential-Difference Equations","authors":"X. Zhu, X. Qi","doi":"10.3103/s1068362324700122","DOIUrl":"https://doi.org/10.3103/s1068362324700122","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study the existence of meromorphic solutions of hyperorder strictly less than 1 to the Fermat-type differential-difference equations, which improves earlier results of such studies.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unconditionality of Periodic Orthonormal Spline Systems in $$boldsymbol{H}^{mathbf{1}}boldsymbol{(mathbb{T})}$$ : Sufficiency $$boldsymbol{H}^{mathbf{1}}boldsymbol{(mathbb{T})}$$ 中周期正交样条系统的无条件性：充分性
IF 0.3 4区 数学
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2024-07-09 DOI: 10.3103/s1068362324700158
L. Hakobyan, K. Keryan
{"title":"Unconditionality of Periodic Orthonormal Spline Systems in $$boldsymbol{H}^{mathbf{1}}boldsymbol{(mathbb{T})}$$ : Sufficiency","authors":"L. Hakobyan, K. Keryan","doi":"10.3103/s1068362324700158","DOIUrl":"https://doi.org/10.3103/s1068362324700158","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We give a geometric characterization of knot sequences <span>((s_{n}))</span>, which is a sufficient condition for the corresponding periodic orthonormal spline system of arbitrary order <span>(k)</span>, <span>(kinmathbb{N})</span>, is an unconditional basis in the atomic Hardy space on the torus <span>(H^{1}(mathbb{T}))</span>.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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