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Norm convergence of subsequences of matrix transform means of Walsh–Fourier series 沃尔什-傅里叶级数的矩阵变换手段子序列的规范收敛性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-06-01 DOI: 10.1007/s10998-024-00584-3
István Blahota
{"title":"Norm convergence of subsequences of matrix transform means of Walsh–Fourier series","authors":"István Blahota","doi":"10.1007/s10998-024-00584-3","DOIUrl":"https://doi.org/10.1007/s10998-024-00584-3","url":null,"abstract":"<p>Let <span>({a_{n}: nin mathbb {P}})</span> be an increasing sequence of positive integers. For every <span>(nin mathbb {P})</span> let <span>({t_{k,a_{n}}: 1le kle a_{n}, kin mathbb {P}})</span> be a finite sequence of non-negative numbers such that </p><span>$$begin{aligned} sum _{k=1}^{a_{n}} t_{k,a_{n}}=1 end{aligned}$$</span><p>holds and </p><span>$$begin{aligned} lim _{nrightarrow infty }t_{k,a_{n}}=0 end{aligned}$$</span><p>is satisfied for any fixed <i>k</i>. Our main result (Theorem 6.5) is that we prove <span>(L_{1})</span>-norm convergence </p><span>$$begin{aligned} sigma _{a_{n}}^{T}(f)rightarrow f end{aligned}$$</span><p>(for example, but not limited to <span>(a_{n}:=2^{n})</span>, see Corollary 6.6 and Sect. 7) with weaker conditions than it was known before for matrix transform means and for some special means, namely Nörlund and weighted ones.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A molecular reconstruction theorem for $$H^{p(cdot )}_{omega }(mathbb {R}^{n})$$ $$H^{p(cdot )}_{omega }(mathbb {R}^{n})$$ 的分子重构定理
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-05-30 DOI: 10.1007/s10998-024-00575-4
Pablo Rocha
{"title":"A molecular reconstruction theorem for $$H^{p(cdot )}_{omega }(mathbb {R}^{n})$$","authors":"Pablo Rocha","doi":"10.1007/s10998-024-00575-4","DOIUrl":"https://doi.org/10.1007/s10998-024-00575-4","url":null,"abstract":"<p>In this article we give a molecular reconstruction theorem for <span>(H_{omega }^{p(cdot )}(mathbb {R}^{n}))</span>. As an application of this result and the atomic decomposition developed in Ho (Tohoku Math J 69 (3), 383–413, 2017) we show that classical singular integrals can be extended to bounded operators on <span>(H_{omega }^{p(cdot )}(mathbb {R}^{n}))</span>. We also prove, for certain exponents <span>(q(cdot ))</span> and certain weights <span>(omega )</span>, that the Riesz potential <span>(I_{alpha })</span>, with <span>(0&lt; alpha &lt; n)</span>, can be extended to a bounded operator from <span>(H^{p(cdot )}_{omega }(mathbb {R}^{n}))</span> into <span>(H^{q(cdot )}_{omega }(mathbb {R}^{n}))</span>, for <span>(frac{1}{p(cdot )}:= frac{1}{q(cdot )} + frac{alpha }{n})</span>.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Description of the symmetric $$H_q$$ -Laguerre–Hahn orthogonal q-polynomials of class one 一级对称 $$H_q$$ -Laguerre-Hahn 正交 q 多项式的描述
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-03-06 DOI: 10.1007/s10998-024-00574-5
Sobhi Jbeli
{"title":"Description of the symmetric $$H_q$$ -Laguerre–Hahn orthogonal q-polynomials of class one","authors":"Sobhi Jbeli","doi":"10.1007/s10998-024-00574-5","DOIUrl":"https://doi.org/10.1007/s10998-024-00574-5","url":null,"abstract":"<p>We study the <span>(H_{q})</span>-Laguerre–Hahn forms <i>u</i>, that is to say those satisfying a <i>q</i>-quadratic <i>q</i>-difference equation with polynomial coefficients (<span>(Phi , Psi , B)</span>): <span>( H_{q}(Phi (x)u) +Psi (x) u+B(x) , big (x^{-1}u(h_{q}u)big )=0,)</span> where <span>(h_q u)</span> is the form defined by <span>(langle h_{q} u,frangle =langle u, f(qx)rangle )</span> for all polynomials <i>f</i> and <span>(H_{q})</span> is the <i>q</i>-derivative operator. We give the definition of the class <i>s</i> of such a form and the characterization of its corresponding orthogonal <i>q</i>-polynomials sequence <span>({P_n}_{nge 0})</span> by the structure relation. As a consequence, we establish the system fulfilled by the coefficients of the structure relation, those of the polynomials <span>(Phi , Psi , B)</span> and the recurrence coefficient <span>(gamma _{n+1}, , n ge 0)</span>, of <span>({P_n}_{nge 0})</span> for the class one in the symmetric case. In addition, we present the complete description of the symmetric <span>(H_{q})</span>-Laguerre–Hahn forms of class <span>(s=1.)</span> The limiting cases are also covered.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140053648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Linear independence on simple abelian varieties 简单无性变上的线性独立性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-02-22 DOI: 10.1007/s10998-024-00573-6
Duc Hiep Pham
{"title":"Linear independence on simple abelian varieties","authors":"Duc Hiep Pham","doi":"10.1007/s10998-024-00573-6","DOIUrl":"https://doi.org/10.1007/s10998-024-00573-6","url":null,"abstract":"<p>In this paper, we establish new results on complex and <i>p</i>-adic linear independence on general simple abelian varieties defined over the field of algebraic numbers <span>(overline{{mathbb {Q}}})</span>. In particular, these results extend some previous results on that concerning elliptic curves and simple abelian varieties with complex multiplication defined over <span>(overline{{mathbb {Q}}})</span>.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139927266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Spanning trees of $$K_{1,4}$$ -free graphs whose reducible stems have few leaves 无$$K_{1,4}$$图的生成树，其可还原茎的叶子很少
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-02-19 DOI: 10.1007/s10998-024-00572-7
Pham Hoang Ha, Le Dinh Nam, Ngoc Diep Pham
{"title":"Spanning trees of $$K_{1,4}$$ -free graphs whose reducible stems have few leaves","authors":"Pham Hoang Ha, Le Dinh Nam, Ngoc Diep Pham","doi":"10.1007/s10998-024-00572-7","DOIUrl":"https://doi.org/10.1007/s10998-024-00572-7","url":null,"abstract":"<p>Let <i>T</i> be a tree; a vertex of degree 1 is a <i>leaf</i> of <i>T</i> and a vertex of degree at least 3 is a <i>branch vertex</i> of <i>T</i>. The <i>reducible stem</i> of <i>T</i> is the smallest subtree that contains all branch vertices of <i>T</i>. In this paper, we give some sharp sufficient conditions for <span>(K_{1,4})</span>-free graphs to have a spanning tree whose reducible stem has few leaves.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139928714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 q-statistical convergence of double sequences 论双重序列的 q 统计收敛性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-01-19 DOI: 10.1007/s10998-023-00556-z
Mohammad Mursaleen, Sabiha Tabassum, Ruqaiyya Fatma
{"title":"On the q-statistical convergence of double sequences","authors":"Mohammad Mursaleen, Sabiha Tabassum, Ruqaiyya Fatma","doi":"10.1007/s10998-023-00556-z","DOIUrl":"https://doi.org/10.1007/s10998-023-00556-z","url":null,"abstract":"<p>In this paper, we study <i>q</i>-statistical convergence for double sequences. The definitions of <i>q</i>-analog of statistical Cauchy and statistical pre-Cauchy for double sequences are given. The necessary and sufficient condition for a double sequence to have different statistical limits is also obtained. We show that a <i>q</i>-statistical convergent sequence is <i>q</i>-statistical Cauchy and vice-versa.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Correction to: On Greenberg’s conjecture for certain real biquadratic fields 更正：关于格林伯格对某些实双曲域的猜想
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-01-09 DOI: 10.1007/s10998-023-00571-0
Abdelkader El Mahi, M’hammed Ziane
{"title":"Correction to: On Greenberg’s conjecture for certain real biquadratic fields","authors":"Abdelkader El Mahi, M’hammed Ziane","doi":"10.1007/s10998-023-00571-0","DOIUrl":"https://doi.org/10.1007/s10998-023-00571-0","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139442842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Non-vanishing and cofiniteness of generalized local cohomology modules 广义局部同调模块的非凡性和同完备性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-01-02 DOI: 10.1007/s10998-023-00567-w
Tran Tuan Nam, Nguyen Minh Tri
{"title":"Non-vanishing and cofiniteness of generalized local cohomology modules","authors":"Tran Tuan Nam, Nguyen Minh Tri","doi":"10.1007/s10998-023-00567-w","DOIUrl":"https://doi.org/10.1007/s10998-023-00567-w","url":null,"abstract":"<p>In this paper, we show some results on the non-vanishing of the generalized local cohomology modules <span>(H^i_I(M,N))</span>. In a Cohen–Macaulay local ring <span>((R,mathop {mathfrak {m}}))</span>, we prove, by using induction on <span>(dim N)</span>, that if <i>M</i>, <i>N</i> are two finitely generated <i>R</i>-modules with <span>({text {id}},M&lt;infty )</span> and <span>({text {Gid}},N&lt;infty )</span>, then <span>(H^{dim R-grade _R({text {Ann}}_RN,M)}_{mathop {mathfrak {m}}}(M,N)ne 0)</span>. We also study the <i>I</i>-cofiniteness of the generalized local cohomology module <span>(H^i_{mathop {mathfrak {m}}}(M,N))</span>.\u0000</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 boundedness of general partial sums 论一般偏和的有界性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-24 DOI: 10.1007/s10998-023-00565-y
Vakhtang Tsagareishvili
{"title":"On the boundedness of general partial sums","authors":"Vakhtang Tsagareishvili","doi":"10.1007/s10998-023-00565-y","DOIUrl":"https://doi.org/10.1007/s10998-023-00565-y","url":null,"abstract":"<p>From S. Banach’s results it follows that even for the function <span>(f(x)=1)</span> <span>((xin [0,1]))</span> the general partial sums of its general Fourier series are not bounded a.e. on [0, 1]. In the present paper, we find conditions for the functions <span>(varphi _n)</span> of an orthonormal system <span>((varphi _n)</span>) under which the partial sums of functions from some differentiable class are bounded. We prove that the obtained results are best possible. We also investigate the properties of subsequences of general orthonormal systems.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139028762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Bifurcation and hybrid control in a discrete predator–prey model with Holling type-IV functional response 具有霍林IV型功能响应的离散捕食者-猎物模型中的分岔和混合控制
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-16 DOI: 10.1007/s10998-023-00568-9
Wenxian Zhang, Shengfu Deng
{"title":"Bifurcation and hybrid control in a discrete predator–prey model with Holling type-IV functional response","authors":"Wenxian Zhang, Shengfu Deng","doi":"10.1007/s10998-023-00568-9","DOIUrl":"https://doi.org/10.1007/s10998-023-00568-9","url":null,"abstract":"<p>In this paper we investigate the 1:1 resonance and the hybrid control in a discrete predator–prey model with Holling-IV functional response, which is derived from a 2-dimensional continuous one of Gause type. When the parameters satisfy some conditions, this discrete model has a positive fixed point, which has a double eigenvalue 1 with geometric multiplicity 1. With the Picard iteration and the time-one map, this discrete one is converted into an ordinary differential system. It is shown that a Bogdanov–Takens bifurcation for this ordinary differential system happens by the bifurcation theory. This implies that this discrete model undergoes a Neimark–Sacker bifurcation and a homoclinic bifurcation. The stability of its fixed point is obtained. Then, the hybrid control strategy is applied to control the stability of this fixed point. Finally, the local phase portraits of these systems are also simulated by the Matlab software.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138693124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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