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Specific properties of Lipschitz class functions Lipschitz 类函数的具体性质
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-10 DOI: 10.1007/s10474-024-01432-z
A. Kashibadze, V. Tsagareishvili
{"title":"Specific properties of Lipschitz class functions","authors":"A. Kashibadze, V. Tsagareishvili","doi":"10.1007/s10474-024-01432-z","DOIUrl":"https://doi.org/10.1007/s10474-024-01432-z","url":null,"abstract":"<p>We consider the Lipschitz class functions on [0, 1]\u0000and special series of their Fourier coefficients with respect to general\u0000orthonormal systems (ONS).\u0000The convergence of classical Fourier series (trigonometric, Haar, Walsh systems) of Lip 1 class functions is a trivial problem and is well known. But general Fourier series, as it is known, even for the function <i>f </i>(<i>x</i>) = 1 does not converge.\u0000On the other hand, we show that such series do not converge with respect to general ONSs. In the paper we find the special conditions on the functions <span>(varphi_{n})</span> of the system <span>((varphi_{n}))</span> such that the above-mentioned series are convergent for any Lipschitz class function. The obtained result is the best possible.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925785","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
Zero free region for spectral averages of Hecke–Maass L-functions Hecke-Maass L 函数谱平均的无零区
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-09 DOI: 10.1007/s10474-024-01430-1
E. M. Sandeep
{"title":"Zero free region for spectral averages of Hecke–Maass L-functions","authors":"E. M. Sandeep","doi":"10.1007/s10474-024-01430-1","DOIUrl":"https://doi.org/10.1007/s10474-024-01430-1","url":null,"abstract":"<p>We provide a non-vanishing region for an infinite sum of weight zero Hecke–Maass <i>L</i>-functions for the full modular group inside the critical strip. For given positive parameters <i>T</i> and <span>(1 leq M ll frac{T}{log T})</span>, <i>T</i> large, we also count the number of Hecke–Maass cusp forms whose <i>L</i>-values are non-zero at any point <i>s</i> in this region and whose spectral parameters <span>(t_j)</span> lie in short intervals.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925784","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 G-Drazin partial order in rings 论环中的 G-Drazin 偏序
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-08 DOI: 10.1007/s10474-024-01429-8
G. Dolinar, B. Kuzma, J. Marovt, D. Mosić
{"title":"On G-Drazin partial order in rings","authors":"G. Dolinar, B. Kuzma, J. Marovt, D. Mosić","doi":"10.1007/s10474-024-01429-8","DOIUrl":"https://doi.org/10.1007/s10474-024-01429-8","url":null,"abstract":"<p>We extend the concept of a G-Drazin inverse from the set <span>(M_n)</span> of all <span>(ntimes n)</span> complex matrices to the set <span>(mathcal{R}^{D})</span> of all Drazin invertible elements in a ring <span>(mathcal{R})</span> with identity. We also generalize a partial order induced by G-Drazin inverses from <span>(M_n)</span> to the set of all regular elements in <span>(mathcal{R}^{D})</span>, study its properties, compare it to known partial orders, and generalize some known results.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925922","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
Products of unipotent matrices of index 2 over division rings 除法环上指数为 2 的单能矩阵的乘积
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-06 DOI: 10.1007/s10474-024-01427-w
M. H. Bien, T. N. Son, P. T. T. Thuy, L. Q. Truong
{"title":"Products of unipotent matrices of index 2 over division rings","authors":"M. H. Bien, T. N. Son, P. T. T. Thuy, L. Q. Truong","doi":"10.1007/s10474-024-01427-w","DOIUrl":"https://doi.org/10.1007/s10474-024-01427-w","url":null,"abstract":"<p>Let <i>D</i> be a division ring. The first aim of this paper is to describe all unipotent matrices of index 2 in the general linear group <span>(mathrm {GL}_n(D))</span> of degree <i>n</i> and in the Vershik–Kerov group <span>(mathrm{GL} _{rm VK}(D))</span>. As a corollary, the subgroups generated by such matrices are investigated. The next aim is to seek a positive integer <i>d</i> such that every matrix in these groups is a product of at most <i>d</i> unipotent matrices of index 2. For example, we show that if every element in the derived subgroup <span>(D')</span> of <span>(D^*=Dbackslash {0})</span> is a product of at most <i>c</i> commutators in <span>(D^*)</span>, then every matrix in <span>(mathrm{GL}_n(D))</span> (resp., <span>(mathrm{GL} _{rm VK}(D))</span>, which is a product of some unipotent matrices of index 2, can be written as a product of at most 4+3<i>c</i> (resp.,5 + 3<i>c</i>) of unipotent matrices of index 2 in <span>(mathrm{GL}_n(D))</span> (resp., <span>(mathrm{GL}_{rm VK}(D)))</span>.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882635","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 first Banach problem concerning condensations of absolute $$kappa$$ -Borel sets onto compacta 关于绝对 $$kappa$ -Borel 集在紧凑集上的凝聚的第一个巴拿赫问题
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-06 DOI: 10.1007/s10474-024-01428-9
A. V. Osipov
{"title":"On the first Banach problem concerning condensations of absolute $$kappa$$ -Borel sets onto compacta","authors":"A. V. Osipov","doi":"10.1007/s10474-024-01428-9","DOIUrl":"https://doi.org/10.1007/s10474-024-01428-9","url":null,"abstract":"<p>It is consistent that the continuum be arbitrary large and no absolute <span>(kappa)</span>-Borel set X of density <span>(kappa)</span>, <span>(aleph_1&lt;kappa&lt;mathfrak{c})</span>,condenses onto a compactum.</p><p>It is consistent that the continuum be arbitrary large and any absolute <span>(kappa)</span>-Borel set X of density <span>(kappa)</span>, <span>(kappaleqmathfrak{c})</span>, containing a closed subspace of the Baire space of weight <span>(kappa)</span>, condenses onto a compactum.</p><p>In particular, applying Brian's results in model theory, we get the following unexpected result. Given any <span>(Asubseteq mathbb{N})</span> with <span>(1in A)</span>, there is a forcing extension in which every absolute <span>(aleph_n)</span>-Borel set, containing a closed subspace of the Baire space of weight <span>(aleph_n)</span>, condenses onto a compactum if and only if <span>(nin A)</span>.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882736","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
Kannappan–Wilson and Van Vleck–Wilson functional equations on semigroups 半群上的 Kannappan-Wilson 和 Van Vleck-Wilson 函数方程
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-06 DOI: 10.1007/s10474-024-01433-y
Y. Aserrar, E. Elqorachi
{"title":"Kannappan–Wilson and Van Vleck–Wilson functional equations on semigroups","authors":"Y. Aserrar, E. Elqorachi","doi":"10.1007/s10474-024-01433-y","DOIUrl":"https://doi.org/10.1007/s10474-024-01433-y","url":null,"abstract":"<p>Let <span>(S)</span> be a semigroup, <span>(Z(S))</span> the center of <span>(S)</span> and <span>(sigma colon S rightarrow S)</span> is an\u0000involutive automorphism. Our main results is that we describe the solutions of\u0000the Kannappan-Wilson functional equation</p><p><span>(int_{S} f(xyt), dmu(t) + int_{S} f(sigma(y)xt), dmu(t)= 2f(x)g(y), x,yin S,)</span></p><p>and the Van Vleck-Wilson functional equation</p><p><span>(int_{S} f(xyt), dmu(t) - int_{S} f(sigma(y)xt), dmu(t)= 2f(x)g(y), x,yin S,)</span></p><p>where <span>(mu)</span> is a measure that is a linear combination of Dirac measures <span>((delta_{z_i})_{iin I})</span>,\u0000such that <span>(z_iin Z(S))</span> for all <span>(iin I)</span>. Interesting consequences of these results are\u0000presented.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882822","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
The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces 离散加权莫雷空间上的哈代-利特尔伍德最大算子
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-22 DOI: 10.1007/s10474-024-01420-3
X. B. Hao, B. D. Li, S. Yang
{"title":"The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces","authors":"X. B. Hao, B. D. Li, S. Yang","doi":"10.1007/s10474-024-01420-3","DOIUrl":"https://doi.org/10.1007/s10474-024-01420-3","url":null,"abstract":"<p>We introduce a discrete version of weighted Morrey spaces,\u0000and discuss the inclusion relations of these spaces. In addition, we obtain the\u0000boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete\u0000weighted Lebesgue spaces by establishing a discrete Calderón-Zygmund decomposition\u0000for weighted <span>(l^1)</span>-sequences. Furthermore, the necessary and sufficient\u0000conditions for the boundedness of the discrete Hardy-Littlewood maximal operators\u0000on discrete weighted Morrey spaces are discussed. Particularly, the necessary\u0000and sufficient conditions are also discussed for the discrete power weights.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800972","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
Sequence-covering maps on submetrizable spaces 可亚元空间上的序列覆盖映射
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01426-x
V. Smolin
{"title":"Sequence-covering maps on submetrizable spaces","authors":"V. Smolin","doi":"10.1007/s10474-024-01426-x","DOIUrl":"https://doi.org/10.1007/s10474-024-01426-x","url":null,"abstract":"<p>A topological space is called submetrizable if it can be mapped onto a metrizable topological space by a continuous one-to-one map. In this paper we answer two questions concerning sequence-covering maps on submetrizable spaces.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591764","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 unramified Galois 2-groups over $$mathbb{Z}_2$$ -extensions of some imaginary biquadratic number fields 关于一些虚二次数域的$$mathbb{Z}_2$$上的未成帧伽罗瓦2群的扩展
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01425-y
A. Mouhib, S. Rouas
{"title":"On unramified Galois 2-groups over $$mathbb{Z}_2$$ -extensions of some imaginary biquadratic number fields","authors":"A. Mouhib, S. Rouas","doi":"10.1007/s10474-024-01425-y","DOIUrl":"https://doi.org/10.1007/s10474-024-01425-y","url":null,"abstract":"<p>For an imaginary biquadratic number field <span>(K = mathbb Q(sqrt{-q},sqrt d))</span>, where <span>(q&gt;3)</span> is a prime congruent to <span>(3 pmod 8)</span>, and <span>(d)</span> is an odd square-free integer which is not equal to <i>q</i>, let <span>(K_infty)</span> be the cyclotomic <span>(mathbb Z_2)</span>-extension of <span>(K)</span>. For any integer <span>(n geq 0)</span>, we denote by <span>(K_n)</span> the <i>n</i>th layer of <span>(K_infty/K)</span>. We investigate the rank of the 2-class group of <span>(K_n)</span>, then we draw the list of all number fields <i>K</i> such that the Galois group of the maximal unramified pro-2-extension over their cyclotomic <span>(mathbb Z_2)</span>-extension is metacyclic pro-2 group.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591998","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
Approximation by Nörlund means with respect to Vilenkin system in Lebesgue spaces 关于 Lebesgue 空间中 Vilenkin 系统的 Nörlund 方式近似法
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-04-10 DOI: 10.1007/s10474-024-01418-x
N. Anakidze, N. Areshidze, L. Baramidze
{"title":"Approximation by Nörlund means with respect to Vilenkin system in Lebesgue spaces","authors":"N. Anakidze, N. Areshidze, L. Baramidze","doi":"10.1007/s10474-024-01418-x","DOIUrl":"https://doi.org/10.1007/s10474-024-01418-x","url":null,"abstract":"<p>We improve and complement a result by Móricz and Siddiqi [20].\u0000In particular, we prove that their estimate of the Nörlund means with respect to\u0000the Vilenkin system holds also without their additional condition. Moreover, we\u0000prove a similar approximation result in Lebesgue spaces for any <span>(1leq p&lt;infty)</span>.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591863","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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