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Mediterranean Journal of Mathematics最新文献

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Positive Solutions to a Second-Order Sturm–Liouville Problem with Nonlocal Boundary Conditions 具有非局部边界条件的二阶 Sturm-Liouville 问题的正解
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-19 DOI: 10.1007/s00009-024-02716-y
Feng Zhang, HuiJuan Zhu, Fanglei Wang
{"title":"Positive Solutions to a Second-Order Sturm–Liouville Problem with Nonlocal Boundary Conditions","authors":"Feng Zhang, HuiJuan Zhu, Fanglei Wang","doi":"10.1007/s00009-024-02716-y","DOIUrl":"https://doi.org/10.1007/s00009-024-02716-y","url":null,"abstract":"<p>Based on a generalization of the Krasnoselskii’s fixed point theorem and Avery–Peterson fixed point theorem, the object of this paper is to investigate the existence of positive solutions to a second-order Sturm–Liouville problem with derivative term and nonlocal boundary conditions. Also, some examples are given to illustrate our main results.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195268","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
Fock Projections on Mixed Norm Spaces 混合规范空间上的福克投影
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-14 DOI: 10.1007/s00009-024-02715-z
Yongqing Liu
{"title":"Fock Projections on Mixed Norm Spaces","authors":"Yongqing Liu","doi":"10.1007/s00009-024-02715-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02715-z","url":null,"abstract":"<p>In this paper, we completely characterize <span>(L^{p,q})</span>-boundedness of (maximal) Fock projections on <span>(mathbb {C})</span> for <span>(1le p,qle infty )</span>. As applications, we identify the dual space of mixed norm space <span>(F_alpha ^{p,q})</span> of entire functions and present an alternative proof of the Littlewood–Paley formula for <span>(F_alpha ^{p,q})</span>.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195236","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
Maximal Regularity for Fractional Difference Equations with Finite Delay on UMD Spaces UMD 空间上具有有限延迟的分数差分方程的最大正则性
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-14 DOI: 10.1007/s00009-024-02717-x
Jichao Zhang, Shangquan Bu
{"title":"Maximal Regularity for Fractional Difference Equations with Finite Delay on UMD Spaces","authors":"Jichao Zhang, Shangquan Bu","doi":"10.1007/s00009-024-02717-x","DOIUrl":"https://doi.org/10.1007/s00009-024-02717-x","url":null,"abstract":"<p>In this paper, we study the <span>(ell ^p)</span>-maximal regularity for the fractional difference equation with finite delay: </p><span>$$begin{aligned} left{ begin{array}{ll} Delta ^{alpha }u(n)=Au(n)+B u(n-lambda )+f(n), nin {mathbb {N}}_0, lambda in {mathbb {N}}; u(i)=0, i=-lambda , -lambda +1,cdots , 1, 2, end{array} right. end{aligned}$$</span><p>where <i>A</i> and <i>B</i> are bounded linear operators defined on a Banach space <i>X</i>, <span>(f:{mathbb {N}}_0rightarrow X)</span> is an <i>X</i>-valued sequence and <span>(2&lt;alpha &lt;3)</span>. We introduce an operator theoretical method based on the notion of <span>(alpha )</span>-resolvent sequence of bounded linear operators, which gives an explicit representation of solution. Further, using Blunck’s operator-valued Fourier multipliers theorems on <span>(ell ^p(mathbb {Z}; X))</span>, we completely characterize the <span>(ell ^p)</span>-maximal regularity of solution when <span>(1&lt; p &lt; infty )</span> and <i>X</i> is a UMD space.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195233","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
Persistent Homology with Selective Rips Complexes Detects Geodesic Circles 用选择性 Rips 复合物检测大地圆的持久同源性
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-07 DOI: 10.1007/s00009-024-02706-0
Žiga Virk
{"title":"Persistent Homology with Selective Rips Complexes Detects Geodesic Circles","authors":"Žiga Virk","doi":"10.1007/s00009-024-02706-0","DOIUrl":"https://doi.org/10.1007/s00009-024-02706-0","url":null,"abstract":"<p>This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of <span>(S^1)</span>) and a bottleneck loop (meaning that each of its perturbations increases the length) in a geodesic space using persistent homology. Under fairly mild conditions, we show that such a loop either terminates a 1-dimensional homology class or gives rise to a 2-dimensional homology class in persistent homology. The main tool in this detection technique are selective Rips complexes, new custom made complexes that function as an appropriate combinatorial lens for persistent homology to detect the above mentioned loops. The main argument is based on a new concept of a local winding number, which turns out to be an invariant of certain homology classes.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947066","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
Properties of a Partial Fredholm Integro-differential Equations with Nonlocal Condition and Algorithms 具有非局部条件的部分弗雷德霍尔积分微分方程的性质与算法
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-06 DOI: 10.1007/s00009-024-02712-2
Dulat S. Dzhumabaev, Anuar D. Dzhumabaev, Anar T. Assanova
{"title":"Properties of a Partial Fredholm Integro-differential Equations with Nonlocal Condition and Algorithms","authors":"Dulat S. Dzhumabaev, Anuar D. Dzhumabaev, Anar T. Assanova","doi":"10.1007/s00009-024-02712-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02712-2","url":null,"abstract":"<p>The paper is concerned with a nonlocal problem for a partial Fredholm integro-differential equation (IDE) of hyperbolic type is investigated. This problem is reduced to a problem containing a family of boundary value problems for the ordinary Fredholm IDEs and some integral relationships. A novel concept of general solution to a family of the ordinary Fredholm IDEs is introduced, and its properties are discussed. A necessary and sufficient condition for the well-posedness of the nonlocal problem for the partial Fredholm integro-differential equation (IDE) of hyperbolic type is obtained, and an algorithm for finding its solution is offered.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947069","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
$$text {CMC-1}$$ Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends 具有康托尔端点的双曲空间和德西特空间中的 $$text {CMC-1}$$ 曲面
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-05 DOI: 10.1007/s00009-024-02707-z
Ildefonso Castro-Infantes, Jorge Hidalgo
{"title":"$$text {CMC-1}$$ Surfaces in Hyperbolic and de Sitter Spaces with Cantor Ends","authors":"Ildefonso Castro-Infantes, Jorge Hidalgo","doi":"10.1007/s00009-024-02707-z","DOIUrl":"https://doi.org/10.1007/s00009-024-02707-z","url":null,"abstract":"<p>We prove that on every compact Riemann surface <i>M</i>, there is a Cantor set <span>(C subset M)</span> such that <span>(M{ setminus }C)</span> admits a proper conformal constant mean curvature one (<span>(text {CMC-1})</span>) immersion into hyperbolic 3-space <span>(mathbb {H}^3)</span>. Moreover, we obtain that every bordered Riemann surface admits an almost proper <span>(text {CMC-1})</span> face into de Sitter 3-space <span>(mathbb {S}_1^3)</span>, and we show that on every compact Riemann surface <i>M</i>, there is a Cantor set <span>(C subset M)</span> such that <span>(M {setminus } C)</span> admits an almost proper <span>(text {CMC-1})</span> face into <span>(mathbb {S}_1^3)</span>. These results follow from different uniform approximation theorems for holomorphic null curves in <span>(mathbb {C}^2 times mathbb {C}^*)</span> that we also establish in this paper.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969673","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 $$nu $$ -Quasiordinary Surface Singularities and Their Resolution 论 $$nu $$ - 准奇异面奇点及其解析
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-05 DOI: 10.1007/s00009-024-02709-x
Fuensanta Aroca, José M. Tornero
{"title":"On $$nu $$ -Quasiordinary Surface Singularities and Their Resolution","authors":"Fuensanta Aroca, José M. Tornero","doi":"10.1007/s00009-024-02709-x","DOIUrl":"https://doi.org/10.1007/s00009-024-02709-x","url":null,"abstract":"<p>Quasiordinary power series were introduced by Jung at the beginning of the 20th century, and were not paid much attention until the work of Lipman and, later on, Gao. They have been thoroughly studied since, as they form a very interesting family of singular varieties, whose properties (or at least many of them) can be encoded in a discrete set of integers, much as what happens with curves. Hironaka proposed a generalization of this concept, the so-called <span>(nu )</span>-quasiordinary power series, which has not been examined in the literature in such detailed way. This paper explores the behavior of these series under the resolution process in the surface case.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947068","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
GNS Construction for $$C^*$$ -Valued Positive Sesquilinear Maps on a quasi *-algebra 准 * 代數上 $$C^*$$ 有值正等次線性映射的 GNS 結構
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-05 DOI: 10.1007/s00009-024-02704-2
Giorgia Bellomonte, Stefan Ivković, Camillo Trapani
{"title":"GNS Construction for $$C^*$$ -Valued Positive Sesquilinear Maps on a quasi *-algebra","authors":"Giorgia Bellomonte, Stefan Ivković, Camillo Trapani","doi":"10.1007/s00009-024-02704-2","DOIUrl":"https://doi.org/10.1007/s00009-024-02704-2","url":null,"abstract":"<p>The GNS construction for positive invariant sesquilinear forms on quasi *-algebra <span>((mathfrak A,{mathfrak A}_{scriptscriptstyle 0}))</span> is generalized to a class of positive sesquilinear maps from <span>(mathfrak Atimes mathfrak A)</span> into a <span>(C^*)</span>-algebra <span>({mathfrak {C}})</span>. The result is a *-representation taking values in a space of operators acting on a certain quasi-normed <span>({mathfrak {C}})</span>-module.\u0000</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947067","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 Fourier–Dunkl Coefficients of Generalized Lipschitz Classes on the Interval $$[-1,1]$$ 论区间 $$[-1,1]$$ 上广义 Lipschitz 类的傅立叶-邓克尔系数
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-05 DOI: 10.1007/s00009-024-02710-4
Othman Tyr
{"title":"On the Fourier–Dunkl Coefficients of Generalized Lipschitz Classes on the Interval $$[-1,1]$$","authors":"Othman Tyr","doi":"10.1007/s00009-024-02710-4","DOIUrl":"https://doi.org/10.1007/s00009-024-02710-4","url":null,"abstract":"<p>In this paper, we consider <span>(mathcal {E})</span> the set of all infinitely differentiable functions with compact support included on the interval <span>(I=[-1,1])</span>. We use the distributions in <span>(mathcal {E})</span>, as a tool to prove the continuity of the Dunkl operator and the Dunkl translation. Some properties of the modulus of smoothness related to the Dunkl operator are verified. By means of generalized Dunkl–Lipschitz conditions on Dunkl–Sobolev spaces, a result of Younis on the torus, which is an analog of Titchmarsh’s theorem, is deduced as a special case. In addition, certain conditions and a characterization of the Dini–Lipschitz classes on <i>I</i> in terms of the behavior of their Fourier–Dunkl coefficients are derived.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947070","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
Characterized Subgroups Related to some Non-arithmetic Sequence of Integers 与某些非算术整数序列相关的特征子群
IF 1.1 3区 数学
Mediterranean Journal of Mathematics Pub Date : 2024-08-03 DOI: 10.1007/s00009-024-02708-y
Pratulananda Das, Ayan Ghosh
{"title":"Characterized Subgroups Related to some Non-arithmetic Sequence of Integers","authors":"Pratulananda Das, Ayan Ghosh","doi":"10.1007/s00009-024-02708-y","DOIUrl":"https://doi.org/10.1007/s00009-024-02708-y","url":null,"abstract":"<p>A subgroup <i>H</i> of the circle group <span>({mathbb {T}})</span> is called characterized by a sequence of integers <span>((u_n))</span> if <span>(H={xin {mathbb {T}}: lim _{nrightarrow infty } u_nx=0})</span>. In this note, we primarily consider a non-arithmetic sequence arising out of an arithmetic sequence in line of Bíró et al. (Stud Sci Math Hung 38: 97–113, 2001) and investigate the corresponding characterized subgroup thoroughly which includes its cardinality aspects. The whole investigation reiterates that these characterized subgroups are infinitely generated unbounded torsion countable subgroups of the circle group <span>({mathbb {T}})</span>. Finally, we delve into certain structure theoretic observations.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885702","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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