Journal of the London Mathematical Society-Second Series最新文献_第2页

Solvability and uniqueness of solution of generalized ★ $star$ -Sylvester equations with arbitrary coefficients

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-18 DOI: 10.1112/jlms.70129

Fernando De Terán, Bruno Iannazzo

{"title":"Solvability and uniqueness of solution of generalized \u0000 \u0000 ★\u0000 $star$\u0000 -Sylvester equations with arbitrary coefficients","authors":"Fernando De Terán, Bruno Iannazzo","doi":"10.1112/jlms.70129","DOIUrl":"https://doi.org/10.1112/jlms.70129","url":null,"abstract":"We analyze the consistency and uniqueness of solution of the generalized <math>\u0000 <semantics>\u0000 <mi>★</mi>\u0000 <annotation>$star$</annotation>\u0000 </semantics></math>-Sylvester equation <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>X</mi>\u0000 <mi>B</mi>\u0000 <mo>+</mo>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>X</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 <mi>D</mi>\u0000 <mo>=</mo>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$AXB+CX^star D=E$</annotation>\u0000 </semantics></math>, with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>,</mo>\u0000 <mi>B</mi>\u0000 <mo>,</mo>\u0000 <mi>C</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$A,B,C, D$</annotation>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> being complex matrices (and <math>\u0000 <semantics>\u0000 <mi>★</mi>\u0000 <annotation>$star$</annotation>\u0000 </semantics></math> being either the transpose or the conjugate transpose). In particular, we obtain characterizations for the equation to have at most one solution and to be consistent for any right-hand side. Such characterizations are given in terms of spectral properties of the matrix pencils <math>\u0000 <semantics>\u0000 <mfenced>\u0000 <mtable>\u0000 <mtr>\u0000 <mtd>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mtd>\u0000 <mtd>\u0000 <msup>\u0000 <mi>B</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 </mtd>\u0000 </mtr>\u0000 <mtr>\u0000 <mtd>\u0000 <mi>A</mi>\u0000 </mtd>\u0000 <mtd>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 </mtd>\u0000 </mtr>\u0000 </mtable>\u0000 </mfenced>\u0000 <annotation>$left[begin{smallmatrix}lambda D^star & B^star A & lambda Cend{smallmatrix}right]$</annota","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638898","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}

引用次数: 0

Shift orbits for elementary representations of Kronecker quivers

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70122

Daniel Bissinger

{"title":"Shift orbits for elementary representations of Kronecker quivers","authors":"Daniel Bissinger","doi":"10.1112/jlms.70122","DOIUrl":"https://doi.org/10.1112/jlms.70122","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>∈</mo>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mrow>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$r in mathbb {N}_{geqslant 3}$</annotation>\u0000 </semantics></math>. We denote by <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <annotation>$K_r$</annotation>\u0000 </semantics></math> the wild <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-Kronecker quiver with <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> arrows <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <mn>1</mn>\u0000 <mo>⟶</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$gamma _i colon 1 longrightarrow 2$</annotation>\u0000 </semantics></math> and consider the action of the group <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mo>⊆</mo>\u0000 <mo>Aut</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$G_r subseteq operatorname{Aut}(mathbb {Z}^2)$</annotation>\u0000 </semantics></math> generated by <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>⟶</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595308","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}

引用次数: 0

Variational stabilization of degenerate p $p$ -elasticae

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70096

Tatsuya Miura, Kensuke Yoshizawa

{"title":"Variational stabilization of degenerate \u0000 \u0000 p\u0000 $p$\u0000 -elasticae","authors":"Tatsuya Miura, Kensuke Yoshizawa","doi":"10.1112/jlms.70096","DOIUrl":"https://doi.org/10.1112/jlms.70096","url":null,"abstract":"A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-elasticae. It was known that in the nondegenerate regime <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$pin (1,2]$</annotation>\u0000 </semantics></math>, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$pin (2,infty)$</annotation>\u0000 </semantics></math> there emerge uncountably many local minimizers with diverging energy.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595305","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}

引用次数: 0

Size-Ramsey numbers of graphs with maximum degree three

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70116

Nemanja Draganić, Kalina Petrova

{"title":"Size-Ramsey numbers of graphs with maximum degree three","authors":"Nemanja Draganić, Kalina Petrova","doi":"10.1112/jlms.70116","DOIUrl":"https://doi.org/10.1112/jlms.70116","url":null,"abstract":"The size-Ramsey number <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mi>r</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$hat{r}(H)$</annotation>\u0000 </semantics></math> of a graph <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> is the smallest number of edges a (host) graph <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> can have, such that for any red/blue colouring of <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, there is a monochromatic copy of <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> in <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. Recently, Conlon, Nenadov and Trujić showed that if <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> is a graph on <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> vertices and maximum degree three, then <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mi>r</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>O</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>8</mn>\u0000 <mo>/</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$hat{r}(H) = O(n^{8/5})$</annotation>\u0000 </semantics></math>, improving upon the upper bound of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70116","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595307","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}

引用次数: 0

Ergodic averages along sequences of slow growth

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70124

Kaitlyn Loyd, Sovanlal Mondal

{"title":"Ergodic averages along sequences of slow growth","authors":"Kaitlyn Loyd, Sovanlal Mondal","doi":"10.1112/jlms.70124","DOIUrl":"https://doi.org/10.1112/jlms.70124","url":null,"abstract":"We consider pointwise almost everywhere convergence of weighted ergodic averages along the sequence <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math> denotes the number of prime factors of <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$ n$</annotation>\u0000 </semantics></math> counted with multiplicities. It was previously shown that a pointwise ergodic theorem for <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math> functions does not hold along <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. We classify the strength of this divergence by proving a double-logarithmic pointwise ergodic theorem for <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> functions along <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. This contrasts the behavior of Khintchine-type averages, for which, under any weaker form of averaging, there exists a bounded measurable function for which almost everywhere convergence fails. Moreover, we show that certain perturbations of increasing subpolynomial sequences fail to satisfy a pointwise ergodic theorem, yielding natural new examples of such sequences.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70124","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595309","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}

引用次数: 0

Einstein metrics on aligned homogeneous spaces with two factors

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-10 DOI: 10.1112/jlms.70120

Jorge Lauret, Cynthia Will

{"title":"Einstein metrics on aligned homogeneous spaces with two factors","authors":"Jorge Lauret, Cynthia Will","doi":"10.1112/jlms.70120","DOIUrl":"https://doi.org/10.1112/jlms.70120","url":null,"abstract":"Given two homogeneous spaces of the form <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$G_1/K$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$G_2/K$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$G_1$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math> are compact simple Lie groups, we study the existence problem for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$G_1times G_2$</annotation>\u0000 </semantics></math>-invariant Einstein metrics on the homogeneous space <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$M=G_1times G_2/K$</annotation>\u0000 </semantics></math>. For the large subclass <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathcal {C}$</annotation>\u0000 </semantics></math> of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and nonexistence pieces of <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathcal {C}$</annotation>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594912","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}

引用次数: 0

Rigidity of quantum algebras

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-08 DOI: 10.1112/jlms.70118

Akaki Tikaradze

{"title":"Rigidity of quantum algebras","authors":"Akaki Tikaradze","doi":"10.1112/jlms.70118","DOIUrl":"https://doi.org/10.1112/jlms.70118","url":null,"abstract":"Given an associative <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbb {C}$</annotation>\u0000 </semantics></math>-algebra <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, we call <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> strongly rigid if for any pair of finite subgroups of its automorphism groups <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>,</mo>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>$G, H$</annotation>\u0000 </semantics></math>, such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mi>G</mi>\u0000 </msup>\u0000 <mo>≅</mo>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mi>H</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$A^Gcong A^H$</annotation>\u0000 </semantics></math>, then <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid. We also solve the inverse Galois problem for a wide class of rational Cherednik algebras that includes all (simple) classical generalized Weyl algebras, and also for quantum tori. Finally, we show that the Picard group of an <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional quantum torus is isomorphic to the group of its outer automorphisms.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70118","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581758","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}

引用次数: 0

Higher order Lipschitz Sandwich theorems

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-07 DOI: 10.1112/jlms.70121

Terry Lyons, Andrew D. McLeod

{"title":"Higher order Lipschitz Sandwich theorems","authors":"Terry Lyons, Andrew D. McLeod","doi":"10.1112/jlms.70121","DOIUrl":"https://doi.org/10.1112/jlms.70121","url":null,"abstract":"We investigate the consequence of two <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Lip</mi>\u0000 <mo>(</mo>\u0000 <mi>γ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${mathrm{Lip}}(gamma)$</annotation>\u0000 </semantics></math> functions, in the sense of Stein, being close throughout a subset of their domain. A particular consequence of our results is the following. Given <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>></mo>\u0000 <mi>ε</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$K_0 > varepsilon > 0$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>></mo>\u0000 <mi>η</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$gamma > eta > 0$</annotation>\u0000 </semantics></math>, there is a constant <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>=</mo>\u0000 <mi>δ</mi>\u0000 <mo>(</mo>\u0000 <mi>γ</mi>\u0000 <mo>,</mo>\u0000 <mi>η</mi>\u0000 <mo>,</mo>\u0000 <mi>ε</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$delta = delta (gamma,eta,varepsilon,K_0) > 0$</annotation>\u0000 </semantics></math> for which the following is true. Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Sigma subset {mathbb {R}}^d$</annotation>\u0000 </semantics></math> be closed and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>h</mi>\u0000 <mo>:</mo>\u0000 <mi>Σ</mi>\u0000 <mo>→</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$f, h: Sigma rightarrow {mathbb {R}}$</annotation>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70121","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143571227","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}

引用次数: 0

Bounds on Fourier coefficients and global sup-norms for Siegel cusp forms of degree 2

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-07 DOI: 10.1112/jlms.70119

Félicien Comtat, Jolanta Marzec-Ballesteros, Abhishek Saha

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引用次数: 0

Substitutions on compact alphabets

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-06 DOI: 10.1112/jlms.70123

Neil Mañibo, Dan Rust, James J. Walton

引用次数: 0