Journal of Mathematical Analysis and Applications最新文献

{"title":"Shrinking Ricci solitons and homology n-spheres","authors":"Chandan Kumar Mondal","doi":"10.1016/j.jmaa.2025.129560","DOIUrl":"10.1016/j.jmaa.2025.129560","url":null,"abstract":"<div><div>In this short note, we find a sufficient curvature condition for a compact, orientable, shrinking Ricci soliton to become an n-homology sphere.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129560"},"PeriodicalIF":1.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799662","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}

{"title":"Geometric nonlinear classification of Lp(μ)-spaces","authors":"Ryotaro Tanaka","doi":"10.1016/j.jmaa.2025.129559","DOIUrl":"10.1016/j.jmaa.2025.129559","url":null,"abstract":"<div><div>In this paper, we study nonlinear classification of Banach spaces with respect to geometric structure spaces. We mainly give classification results on the family of Banach spaces <span><math><mo>{</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo><mo>:</mo><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo><mo>}</mo></math></span> for a localizable measure <em>μ</em>, which extend the known results on <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-spaces. It turns out that <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>-spaces are completely classified by their geometric structure spaces in the infinite-dimensional and localizable case, and that <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> have mutually different geometric structure spaces. Since geometric structure spaces of Banach spaces are invariants of Birkhoff-James orthogonality preservers, the main results in this paper apply to classifying <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>-spaces with respect to the structure of Birkhoff-James orthogonality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129559"},"PeriodicalIF":1.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807742","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}

{"title":"Sticky particles solutions for the attractive pressureless Euler-Poisson system; a projection formula and asymptotic behavior","authors":"B. Becerra ,&nbsp;J. Linderoth ,&nbsp;H. Pesin ,&nbsp;A. Tudorascu ,&nbsp;R. Wassink","doi":"10.1016/j.jmaa.2025.129553","DOIUrl":"10.1016/j.jmaa.2025.129553","url":null,"abstract":"<div><div>In this paper we perform a comprehensive study of the sticky particles solutions to the one-dimensional attractive pressureless Euler-Poisson system. We first provide a Lagrangian map characterization of the sticky particles solutions as projections onto the convex cone of essentially nondecreasing functions in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> by following closely the approach employed earlier by Natile &amp; Savaré for the pressureless Euler case. As a byproduct, we obtain sticky particles solutions for general initial data consisting of Borel probability measures with finite second moment and initial velocities that are square-integrable with respect to said measures. The asymptotic behavior of the sticky particles solutions is the main objective of our work; we obtain explicit exact collapse times into the equilibrium whenever such collapse occurs. In general, we prove that the sticky particles solution converges to the equilibrium in the 1-Wasserstein distance at an explicit rate.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129553"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814841","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}

{"title":"Geodesic distance on Sierpinski-like carpet","authors":"Ying Lu ,&nbsp;Qingcheng Zeng ,&nbsp;Jiajun Xu ,&nbsp;Lifeng Xi","doi":"10.1016/j.jmaa.2025.129541","DOIUrl":"10.1016/j.jmaa.2025.129541","url":null,"abstract":"<div><div>On the Sierpinski-like carpet, we study some conditions to ensure any two points can be connected by a rectifiable path on the carpet and the geodesic distance is comparable to the Manhattan distance. Based on these results, we obtain the Hausdorff dimension of skeleton network of Sierpinski-like carpet.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129541"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799225","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}

{"title":"Lp-estimates for uncentered spherical averages and lacunary maximal functions","authors":"Ankit Bhojak ,&nbsp;Surjeet Singh Choudhary ,&nbsp;Saurabh Shrivastava ,&nbsp;Kalachand Shuin","doi":"10.1016/j.jmaa.2025.129555","DOIUrl":"10.1016/j.jmaa.2025.129555","url":null,"abstract":"<div><div>The primary goal of this paper is to introduce bilinear analogues of uncentered spherical averages, Nikodym averages associated with spheres and the associated bilinear maximal functions. We obtain <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-estimates for uncentered bilinear maximal functions for dimensions <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. Moreover, we also discuss the one-dimensional case. In the process of developing these results, we also establish new and interesting results in the linear case. In particular, we will prove <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-improving properties for single scale averaging operators and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-estimates for lacunary maximal functions in this context.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129555"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807130","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}

{"title":"New q-congruences from a quadratic summation of Gasper and Rahman","authors":"Victor J.W. Guo,&nbsp;Xing-Ye Zhu","doi":"10.1016/j.jmaa.2025.129558","DOIUrl":"10.1016/j.jmaa.2025.129558","url":null,"abstract":"<div><div>By making use of Gasper and Rahman's quadratic summation, the creative microscoping method introduced by the first author and Zudilin, and the Chinese remainder theorem for polynomials, we present two new <em>q</em>-congruences modulo the fourth power of a cyclotomic polynomial, along with a Dwork-type <em>q</em>-congruence. Our results are generalizations of two recent <em>q</em>-congruences due to He and Wang. We also propose four related conjectures on congruences and <em>q</em>-congruences.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129558"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807816","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}

{"title":"Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains","authors":"Nathanael Skrepek ,&nbsp;Dirk Pauly","doi":"10.1016/j.jmaa.2025.129548","DOIUrl":"10.1016/j.jmaa.2025.129548","url":null,"abstract":"<div><div>We investigate the boundary trace operators that naturally correspond to <span><math><mi>H</mi><mo>(</mo><mi>curl</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span>, namely the tangential and twisted tangential trace, where <span><math><mi>Ω</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In particular we regard partial tangential traces, i.e., we look only on a subset Γ of the boundary ∂Ω. We assume both Ω and Γ to be strongly Lipschitz (possibly unbounded). We define the space of all <span><math><mi>H</mi><mo>(</mo><mi>curl</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span> fields that possess a <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> tangential trace in a weak sense and show that the set of all smooth fields is dense in that space, which is a generalization of <span><span>[1]</span></span>. This is especially important for Maxwell's equation with mixed boundary condition as we answer the open problem by Weiss and Staffans in <span><span>[10, Sec. 5]</span></span> for strongly Lipschitz pairs.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129548"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential equations in Ward's calculus","authors":"Ana Luzón ,&nbsp;Manuel A. Morón ,&nbsp;José L. Ramírez","doi":"10.1016/j.jmaa.2025.129557","DOIUrl":"10.1016/j.jmaa.2025.129557","url":null,"abstract":"<div><div>In this paper, we solve some differential equations in the <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> derivative in Ward's sense. We use a special metric in the formal power series ring <span><math><mi>K</mi><mo>[</mo><mo>[</mo><mi>x</mi><mo>]</mo><mo>]</mo></math></span>. The solutions of those equations are given in terms of fixed points for certain contractive maps in our metric framework. Our main tools are Banach's fixed point theorem, the fundamental theorem of calculus, and Barrow's rule for Ward's calculus. Later, we return to the usual differential calculus via Sheffer's expansion of some kind of operators. Finally, we give some examples related, in some sense, to combinatorics.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129557"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807741","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}

{"title":"Some pseudo-spectrum equalities of 2 × 2 unbounded upper triangular operator matrices and applications","authors":"Deyu Wu ,&nbsp;Xinran Liu","doi":"10.1016/j.jmaa.2025.129556","DOIUrl":"10.1016/j.jmaa.2025.129556","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; We investigate the conditions under which&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∪&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; hold and some sufficient conditions are obtained, where the set &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; denotes the pseudo-spectrum, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; denote the approximation pseudo-spectrum and defect pseudo-spectrum, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; denotes the Ammar-Jeribi essential pseudo-spectrum, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; denote the essential approximation pseudo-spectrum and essential defect pseudo-spectrum, respectively. In the end, the main results are applied to the boundary value problem of the plate bending equation, and it is verified that the obtained conclusion is consis","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129556"},"PeriodicalIF":1.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769295","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}

{"title":"A note on smooth rotund norms which are not midpoint locally uniformly rotund","authors":"Carlo Alberto De Bernardi ,&nbsp;Alessandro Preti ,&nbsp;Jacopo Somaglia","doi":"10.1016/j.jmaa.2025.129544","DOIUrl":"10.1016/j.jmaa.2025.129544","url":null,"abstract":"<div><div>We prove that every separable infinite-dimensional Banach space admits a Gâteaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a similar technique, we provide in every infinite-dimensional Banach space with separable dual a Fréchet smooth and weakly uniformly rotund norm which is not midpoint locally uniformly rotund. These two results provide a positive answer to some open problems by A. J. Guirao, V. Montesinos, and V. Zizler.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129544"},"PeriodicalIF":1.2,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815052","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}