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Archiv der Mathematik最新文献

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On the invertibility of bounded operators with a lower bound on reflexive Banach spaces, and applications to (C_{0})-semigroups 自反Banach空间上有下界算子的可逆性及其在(C_{0}) -半群上的应用
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-01-04 DOI: 10.1007/s00013-025-02209-8
Belabbas Madani
{"title":"On the invertibility of bounded operators with a lower bound on reflexive Banach spaces, and applications to (C_{0})-semigroups","authors":"Belabbas Madani","doi":"10.1007/s00013-025-02209-8","DOIUrl":"10.1007/s00013-025-02209-8","url":null,"abstract":"<div><p>We present a new version of an invertibility result for operators satisfying a lower bound condition. The result states that any bounded operator on a reflexive Banach space, which satisfies the lower bound condition, can be extended to a larger reflexive Banach space where it becomes invertible. Furthermore, we provide applications to <span>(C_{0})</span>-semigroups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"305 - 313"},"PeriodicalIF":0.5,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337118","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
Newly appointed editors 新任命的编辑
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-05 DOI: 10.1007/s00013-025-02203-0
{"title":"Newly appointed editors","authors":"","doi":"10.1007/s00013-025-02203-0","DOIUrl":"10.1007/s00013-025-02203-0","url":null,"abstract":"","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"1 - 1"},"PeriodicalIF":0.5,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969465","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
Local (L^2)-boundedness of rough Fourier integral operators with the rough corank condition 粗糙corank条件下粗糙傅立叶积分算子的局部(L^2)有界性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-05 DOI: 10.1007/s00013-025-02207-w
Xiao Yu, Xiangrong Zhu
{"title":"Local (L^2)-boundedness of rough Fourier integral operators with the rough corank condition","authors":"Xiao Yu,&nbsp;Xiangrong Zhu","doi":"10.1007/s00013-025-02207-w","DOIUrl":"10.1007/s00013-025-02207-w","url":null,"abstract":"<div><p>In this paper, we consider a rough Fourier integral operator defined as </p><div><div><span>$$T_{phi ,a}f(x)=int limits _{mathbb {R}^{n}}e^{iphi (x,xi )}a(x,xi )hat{f}(xi )dxi ,$$</span></div></div><p>where the amplitude <span>(ain L^{infty }S^{m}_{rho })</span> and the phase <span>(phi in L^{infty }Phi ^{2})</span> satisfy the rough <i>k</i>-corank condition. The motivation for this problem stems from the regularity of the maximal wave operator. We prove that this operator is bounded from <span>(L^{2})</span> to <span>(L_{text {loc}}^{2})</span> provided </p><div><div><span>$$m&lt;min left{ frac{n(rho -1)}{2},frac{rho }{2}-frac{n+1}{4}right} -frac{krho }{2}.$$</span></div></div></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"315 - 327"},"PeriodicalIF":0.5,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337028","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
Image ratios of word maps and polynomial maps 词映射和多项式映射的图像比率
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-03 DOI: 10.1007/s00013-025-02194-y
Saikat Panja
{"title":"Image ratios of word maps and polynomial maps","authors":"Saikat Panja","doi":"10.1007/s00013-025-02194-y","DOIUrl":"10.1007/s00013-025-02194-y","url":null,"abstract":"<div><p>Let <i>A</i> be a finite group (or a finite algebra), and <span>(omega )</span> be a word map (resp. polynomial map) on <i>n</i> many generators. We define the quantity <span>(|omega (A)|/|A|)</span> as the <i>image ratio of</i> <span>(omega )</span> <i>on</i> <i>A</i> and denote it by <span>(mu (omega ,A))</span>. In this article, we investigate the set <span>(textrm{R}(omega )={mu (omega , A) : A {text { is a finite group}}})</span>, and study the same for the case of rings. We demonstrate the existence of word maps whose set of image ratios is dense in [0, 1] for groups (and rings).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"21 - 28"},"PeriodicalIF":0.5,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969471","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
A note on singularity indices of hyperelliptic fibrations 关于超椭圆型颤振奇异指数的一个注记
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-12-01 DOI: 10.1007/s00013-025-02198-8
Cheng Gong, Zhiming Guo, Xin Lü
{"title":"A note on singularity indices of hyperelliptic fibrations","authors":"Cheng Gong,&nbsp;Zhiming Guo,&nbsp;Xin Lü","doi":"10.1007/s00013-025-02198-8","DOIUrl":"10.1007/s00013-025-02198-8","url":null,"abstract":"<div><p>Let <span>(f: X rightarrow B)</span> be a relatively minimal hyperelliptic fibration of genus <i>g</i>. For such a fibration <i>f</i>, Xiao introduced a series of singularity indices <span>(s_i(f))</span> for <span>(2le i le g+2)</span>. These indices provide an effective way to study the geometry of <i>f</i>. It is known that <span>(s_i(f)ge 0)</span> for <span>(ige 3)</span>, but it is not clear whether <span>(s_2(f))</span> is non-negative. In this note, we construct a sequence of hyperelliptic fibrations with <span>(s_2(f)&lt;0)</span>, where the genus <i>g</i> can be arbitrarily large.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"153 - 163"},"PeriodicalIF":0.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147335971","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
Tor algebra of local rings with decomposable maximal ideal 具有可分解极大理想的局部环的托代数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-27 DOI: 10.1007/s00013-025-02200-3
Saeed Nasseh, Maiko Ono, Yuji Yoshino
{"title":"Tor algebra of local rings with decomposable maximal ideal","authors":"Saeed Nasseh,&nbsp;Maiko Ono,&nbsp;Yuji Yoshino","doi":"10.1007/s00013-025-02200-3","DOIUrl":"10.1007/s00013-025-02200-3","url":null,"abstract":"<div><p>Let <span>((R,mathfrak {m}_R))</span> be a commutative noetherian local ring. Assuming that <span>(mathfrak {m}_R=Ioplus J)</span> is a direct sum decomposition, where <i>I</i> and <i>J</i> are non-zero ideals of <i>R</i>, we describe the structure of the Tor algebra of <i>R</i> in terms of the Tor algebras of the rings <i>R</i>/<i>I</i> and <i>R</i>/<i>J</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"127 - 137"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342384","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
Concentration of norms of random vectors with independent p-sub-exponential coordinates 具有独立p次指数坐标的随机向量的规范集中
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-27 DOI: 10.1007/s00013-025-02199-7
Krzysztof Zajkowski
{"title":"Concentration of norms of random vectors with independent p-sub-exponential coordinates","authors":"Krzysztof Zajkowski","doi":"10.1007/s00013-025-02199-7","DOIUrl":"10.1007/s00013-025-02199-7","url":null,"abstract":"<div><p>We present examples of <i>p</i>-sub-exponential random variables for any positive <i>p</i>. We prove two types of concentration of standard <i>p</i>-norms (2-norm is the Euclidean norm) of random vectors with independent <i>p</i>-sub-exponential coordinates around the Lebesgue <span>(L^p)</span>-norms of these <i>p</i>-norms of random vectors. In the first case <span>(pge 1)</span>, our estimates depend on the dimension <i>n</i> of random vectors. But in the second one for <span>(pge 2)</span>, with an additional assumption, we get an estimate that does not depend on <i>n</i>. In other words, we generalize some known concentration results in the Euclidean case to cases of the <i>p</i>-norms of random vectors with independent <i>p</i>-sub-exponential coordinates.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"209 - 220"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02199-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lie product type formulas for the logarithm 对数的Lie积型公式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-27 DOI: 10.1007/s00013-025-02201-2
Dumitru Popa
{"title":"Lie product type formulas for the logarithm","authors":"Dumitru Popa","doi":"10.1007/s00013-025-02201-2","DOIUrl":"10.1007/s00013-025-02201-2","url":null,"abstract":"<div><p>In this paper, we prove various Lie product type formulas for the logarithm. A sample result: Let <span>(kge 2)</span> be a natural number, <span>(X_{1})</span>,..., <span>(X_{k})</span>, <i>Y</i> Banach algebras with unit and <span>(T:X_{1}times cdot cdot cdot times X_{k}rightarrow Y)</span> a continuous <i>k</i>-linear operator such that <span>(Tleft( textbf{1},...,textbf{1}right) =textbf{1})</span>. Let <span>(left( a_{n}right) _{nin mathbb {N}})</span> be a sequence of natural numbers with <span>( lim _{nrightarrow infty }a_{n}=infty )</span>. Then for all <span>(left( x_{1},...,x_{k}right) in X_{1}times cdot cdot cdot times X_{k})</span> we have </p><div><div><span>$$begin{aligned} &amp; lim limits _{nrightarrow infty }left[ Tleft( textbf{1}+ln left( textbf{1}+frac{x_{1}}{a_{n}}right) ,...,textbf{1}+ln left( textbf{1}+ frac{x_{k}}{a_{n}}right) right) right] ^{a_{n}} &amp; quad =e^{Tleft( x_{1},textbf{1},...,textbf{1}right) +Tleft( textbf{1},x_{2},textbf{1},...,textbf{1}right) +cdot cdot cdot +Tleft( textbf{1},...,textbf{1},x_{k}right) }. end{aligned}$$</span></div></div></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"177 - 186"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342383","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
Stability estimate for an inverse potential problem in time-fractional diffusion problem 时间分数扩散问题中逆势问题的稳定性估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-26 DOI: 10.1007/s00013-025-02185-z
Hamza Kahlaoui
{"title":"Stability estimate for an inverse potential problem in time-fractional diffusion problem","authors":"Hamza Kahlaoui","doi":"10.1007/s00013-025-02185-z","DOIUrl":"10.1007/s00013-025-02185-z","url":null,"abstract":"<div><p>We investigate the inverse problem of identifying a space-depen- dent potential in a Caputo time-fractional diffusion equation from boundary observations. Our analysis establishes a maximum principle for subdiffusion equations with non-homogeneous Neumann boundary conditions, demonstrating the positivity of solutions under specific assumptions on the boundary data. Building upon this result, we leverage the Gâteaux differentiability of the forward map and the non-vanishing property of its derivative to derive a local Lipschitz stability estimate for the inverse potential problem. This provides a rigorous foundation for the stable reconstruction of the potential, highlighting the interplay between fractional dynamics and stability in inverse problems.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"87 - 105"},"PeriodicalIF":0.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969474","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
The median trick does not help for fully nested scrambling 中值技巧对完全嵌套的置乱没有帮助
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-11-26 DOI: 10.1007/s00013-025-02205-y
Takashi Goda, Kosuke Suzuki
{"title":"The median trick does not help for fully nested scrambling","authors":"Takashi Goda,&nbsp;Kosuke Suzuki","doi":"10.1007/s00013-025-02205-y","DOIUrl":"10.1007/s00013-025-02205-y","url":null,"abstract":"<div><p>In randomized quasi-Monte Carlo methods for numerical integration, average estimators based on digital nets with fully nested and linear scramblings, respectively, are known to exhibit the same variance. In this note, we show that this equivalence does not extend to the median estimators. Specifically, while the median estimator with linear scrambling can achieve faster convergence for smooth integrands, the median estimator with fully nested scrambling does not exhibit this advantage.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 2","pages":"221 - 230"},"PeriodicalIF":0.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342315","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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