Journal of the London Mathematical Society-Second Series最新文献

{"title":"Compact and finite-type support in the homology of big mapping class groups","authors":"Martin Palmer,&nbsp;Xiaolei Wu","doi":"10.1112/jlms.70258","DOIUrl":"10.1112/jlms.70258","url":null,"abstract":"<p>For any infinite-type surface <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a <i>compact</i> subsurface; or (ii) a <i>finite-type</i> subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> is positive (including infinite) and a partial answer when the genus of <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> is zero. Our methods involve the notion of <i>shiftable subsurfaces</i> as well as homological stability for mapping class groups of finite-type surfaces.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70258","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the stable radical of the module category for special biserial algebras","authors":"Suyash Srivastava,&nbsp;Vinit Sinha,&nbsp;Amit Kuber","doi":"10.1112/jlms.70275","DOIUrl":"10.1112/jlms.70275","url":null,"abstract":"&lt;p&gt;Suppose that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Lambda$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a special biserial algebra over an algebraically closed field. Schröer showed that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Lambda$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is domestic, then the radical of the category of finitely generated (left) &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Lambda$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-modules is nilpotent, and the least ordinal, denoted as &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;st&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathrm{st}(Lambda)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where the decreasing sequence of powers of the radical stabilizes satisfies &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;st&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathrm{st}(Lambda)&lt;omega ^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. With Gupta and Sardar, the third author conjectured that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Lambda$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has at least one band, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mi&gt;st&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$omega leqslant mathrm{st}(Lambda)&lt;omega ^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; even when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Lambda$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is nondomestic. In this paper, we settle this conjecture in the affirmative. We also describe an algorithm to compute &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;st&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathrm{st}(Lambda)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; up to a ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounded ideal triangulations of infinite Riemann surfaces","authors":"Dragomir Šarić,&nbsp;Casey Whitney","doi":"10.1112/jlms.70276","DOIUrl":"10.1112/jlms.70276","url":null,"abstract":"<p>We introduce a notion of a bounded ideal triangulation of an infinite Riemann surface and parameterize Teichmüller spaces of infinite surfaces which allow bounded triangulations. We prove that our parameterization is real-analytic. Riemann surfaces with bounded geometry and countably many punctures belong to the class of surfaces with bounded ideal triangulations. In comparison, the Fenchel–Nielsen parameterization for surfaces with bounded geometry is not known, while the Fenchel–Nielsen parameterization for surfaces with bounded pants decompositions is known as a homeomorphism but it is not known whether it is real-analytic.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of shifts, interpolation, and spectrum of atomic measures","authors":"Alexander Ulanovskii,&nbsp;Ilya Zlotnikov","doi":"10.1112/jlms.70267","DOIUrl":"10.1112/jlms.70267","url":null,"abstract":"<p>We ask which functions <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$mathcal {G}$</annotation>\u0000 </semantics></math> and separated sets <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> have the property that the <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>-shifts of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$mathcal {G}$</annotation>\u0000 </semantics></math> form an unconditional basis in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^p({mathbb {R}})$</annotation>\u0000 </semantics></math>-closure of their span for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>[</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$pin [1,infty]$</annotation>\u0000 </semantics></math>. The main result establishes the equivalence of this property to each of the two seemingly unrelated conditions: <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> is a set of interpolation for certain Paley–Wiener spaces and the nonexistence of certain measures with given support and spectrum. As a consequence, we answer the question for wide classes of functions <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$mathcal {G}$</annotation>\u0000 </semantics></math> and sets <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>. In particular, we show the connection between the property and the nonexistence of certain crystalline measures.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70267","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp bounds for rainbow matchings in hypergraphs","authors":"Cosmin Pohoata,&nbsp;Lisa Sauermann,&nbsp;Dmitrii Zakharov","doi":"10.1112/jlms.70252","DOIUrl":"10.1112/jlms.70252","url":null,"abstract":"&lt;p&gt;Suppose that we are given matchings &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;.&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M_1,ldots.,M_N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of size &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;annotation&gt;$t$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in some &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-uniform hypergraph, and let us think of each matching having a different color. How large does &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;annotation&gt;$N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; need to be (in terms of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;annotation&gt;$t$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) such that we can always find a rainbow matching of size &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;annotation&gt;$t$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;? This problem was first introduced by Aharoni and Berger, and has since been studied by several different authors. For example, Alon discovered an intriguing connection with the Erdős–Ginzburg–Ziv problem from additive combinatorics, which implies certain lower bounds for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;annotation&gt;$N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For any fixed uniformity &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r geqslant 3$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we answer this problem up to constant factors depending on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, showing that the answer is on the order of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$t^{r}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Furthermore, for any fixed &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;annotation&gt;$t$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144894146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The lower \u0000 \u0000 p\u0000 $p$\u0000 -series of analytic pro-\u0000 \u0000 p\u0000 $p$\u0000 groups and Hausdorff dimension","authors":"Iker de las Heras,&nbsp;Benjamin Klopsch,&nbsp;Anitha Thillaisundaram","doi":"10.1112/jlms.70271","DOIUrl":"10.1112/jlms.70271","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-adic analytic pro-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; group of dimension &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;annotation&gt;$d$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with lower &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-series &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {L} colon P_i(G), ,i in mathbb {N}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We produce an approximate series which descends regularly in strata and whose terms deviate from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$P_i(G)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in a uniformly bounded way. This brings to light a new set of rational invariants &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mstyle&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mstyle&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70271","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144894142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlocal gradients: Fundamental theorem of calculus, Poincaré inequalities, and embeddings","authors":"José Carlos Bellido,&nbsp;Carlos Mora-Corral,&nbsp;Hidde Schönberger","doi":"10.1112/jlms.70277","DOIUrl":"10.1112/jlms.70277","url":null,"abstract":"<p>We address the study of nonlocal gradients defined through general radial kernels <span></span><math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math>. Our investigation focuses on the properties of the associated function spaces, which depend on the characteristics of the kernel function. Specifically, even with minimal assumptions on <span></span><math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math>, we establish Poincaré inequalities and compact embeddings into Lebesgue spaces. Additionally, we present a fundamental theorem of calculus that enables us to recover a function from its nonlocal gradient through a convolution. This is used to demonstrate embeddings into Orlicz spaces and spaces of continuous functions that mirror the well-known Sobolev and Morrey inequalities for classical gradients. Finally, we establish conditions for inclusions and equality of spaces associated to different kernels.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Self-similar instability and forced nonuniqueness: An application to the 2D euler equations","authors":"Michele Dolce,&nbsp;Giulia Mescolini","doi":"10.1112/jlms.70274","DOIUrl":"10.1112/jlms.70274","url":null,"abstract":"<p>Building on an approach introduced by Golovkin in the ’60s, we show that nonuniqueness in some forced partial differential equations is a direct consequence of the existence of a self-similar linearly unstable eigenvalue: the key point is a clever choice of the forcing term removing complicated nonlinear interactions. We use this method to give a short and self-contained proof of nonuniqueness in 2D perfect fluids, first obtained in Vishik's groundbreaking result. In particular, we present a direct construction of a forced self-similar unstable vortex, where we treat perturbatively the self-similar operator in a new and more quantitative way.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70274","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144881090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local spectral theory for subordinated operators: The Cesàro operator and beyond","authors":"Eva A. Gallardo-Gutiérrez,&nbsp;F. Javier González-Doña","doi":"10.1112/jlms.70273","DOIUrl":"10.1112/jlms.70273","url":null,"abstract":"<p>We study local spectral properties for subordinated operators arising from <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$C_0$</annotation>\u0000 </semantics></math>-semigroups. Specifically, if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>⩾</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$mathcal {T}=(T_t)_{tgeqslant 0}$</annotation>\u0000 </semantics></math> is a <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$C_0$</annotation>\u0000 </semantics></math>-semigroup acting boundedly on a complex Banach space and\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sequences suffice for pointfree uniform completions","authors":"Graham Manuell","doi":"10.1112/jlms.70272","DOIUrl":"10.1112/jlms.70272","url":null,"abstract":"<p>Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70272","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}