{"title":"Irregular sampling for hyperbolic secant type functions","authors":"Anton Baranov , Yurii Belov","doi":"10.1016/j.aim.2024.109981","DOIUrl":"10.1016/j.aim.2024.109981","url":null,"abstract":"<div><div>We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., <span><math><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>a</mi><mi>x</mi></mrow></msup><mo>+</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>b</mi><mi>x</mi></mrow></msup><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>, <span><math><mrow><mi>Re</mi></mrow><mspace></mspace><mi>a</mi><mo>,</mo><mrow><mi>Re</mi></mrow><mspace></mspace><mi>b</mi><mo>></mo><mn>0</mn></math></span>. A criterion for half-regular sampling is obtained: for a separated <span><math><mi>Λ</mi><mo>⊂</mo><mi>R</mi></math></span> the Gabor system <span><math><mi>G</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>Λ</mi><mo>×</mo><mi>α</mi><mi>Z</mi><mo>)</mo></math></span> is a frame in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> if and only if <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mi>Λ</mi><mo>)</mo><mo>></mo><mi>α</mi></math></span> where <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mi>Λ</mi><mo>)</mo></math></span> is the usual (Beurling) lower density of Λ. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by <em>g</em> is given.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109981"},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Curvature operators and rational cobordism","authors":"Renato G. Bettiol , McFeely Jackson Goodman","doi":"10.1016/j.aim.2024.109995","DOIUrl":"10.1016/j.aim.2024.109995","url":null,"abstract":"<div><div>We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109995"},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prandtl-Batchelor flows on an annulus","authors":"Mingwen Fei , Chen Gao , Zhiwu Lin , Tao Tao","doi":"10.1016/j.aim.2024.109994","DOIUrl":"10.1016/j.aim.2024.109994","url":null,"abstract":"<div><div>For steady two-dimensional Navier-Stokes flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in the inviscid limit, the vorticity is constant inside the eddy. In this paper, we consider the generalized Prandtl-Batchelor theory for the forced steady Navier-Stokes equations on an annulus. First, we observe that in the limit of infinite Reynolds number, if the streamlines of forced steady Navier-Stokes solutions on an annulus are nested closed, then the inviscid limit is a rotating shear flow uniquely determined by the external force and boundary conditions. We call solutions of steady Navier-Stokes equations with the above property Prandtl-Batchelor flows. Then, by constructing higher order approximate solutions of the forced steady Navier-Stokes equations and establishing the validity of Prandtl boundary layer expansion, we give a rigorous proof of the existence of Prandtl-Batchelor flows on an annulus with the wall velocities slightly different from the rigid-rotations along the same direction.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109994"},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The inequalities of Chern classes and Riemann-Roch type inequalities","authors":"Xing Lu, Jian Xiao","doi":"10.1016/j.aim.2024.109982","DOIUrl":"10.1016/j.aim.2024.109982","url":null,"abstract":"<div><div>Motivated by Kollár-Matsusaka's Riemann-Roch type inequalities, applying effective very ampleness of adjoint bundles on Fujita conjecture and log-concavity given by Khovanskii-Teissier inequalities, we show that for any partition <em>λ</em> of the positive integer <em>d</em> there exists a universal bivariate polynomial <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> which has <span><math><mi>deg</mi><mo></mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>≤</mo><mi>d</mi></math></span> and whose coefficients depend only on <em>n</em> and <em>λ</em>, such that for any projective manifold <em>X</em> of dimension <em>n</em> and any ample line bundle <em>L</em> on <em>X</em>,<span><span><span><math><mrow><mo>|</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>⋅</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>d</mi></mrow></msup><mo>|</mo></mrow><mo>≤</mo><mfrac><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>⋅</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><msup><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mfrac><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is the canonical bundle of <em>X</em> and <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the monomial Chern class given by the partition <em>λ</em>. As a special case, when <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> or <span><math><mo>−</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is ample, this implies that there exists a constant <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> depending only on <em>n</em> such that for any monomial Chern classes of top degree, the Chern number ratios satisfy the following inequality<span><span><span><math><mrow><mo>|</mo><mfrac><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><mo>|</mo></mrow><mo>≤</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo></math></span></span></span> which recovers a recent result of Du-Sun. The main result also yields an asymptotic version of the sharper Riemann-Roch type inequality. Furthermore, using similar method we also obtain inequalities for","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109982"},"PeriodicalIF":1.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Brown-Peterson spectrum is not E2(p2+2) at odd primes","authors":"Andrew Senger","doi":"10.1016/j.aim.2024.109996","DOIUrl":"10.1016/j.aim.2024.109996","url":null,"abstract":"<div><div>We show that the odd-primary Brown-Peterson spectrum BP does not admit the structure of an <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mo>)</mo></mrow></msub></math></span> ring spectrum and that there can be no map <span><math><mrow><mi>MU</mi></mrow><mo>→</mo><mrow><mi>BP</mi></mrow></math></span> of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>3</mn></mrow></msub></math></span> ring spectra. We also prove the same results for truncated Brown-Peterson spectra <span><math><mrow><mi>BP</mi></mrow><mo>〈</mo><mi>n</mi><mo>〉</mo></math></span> of height <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. This extends results of Lawson at the prime 2.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109996"},"PeriodicalIF":1.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefan Glock , David Munhá Correia , Benny Sudakov
{"title":"Hamilton cycles in pseudorandom graphs","authors":"Stefan Glock , David Munhá Correia , Benny Sudakov","doi":"10.1016/j.aim.2024.109984","DOIUrl":"10.1016/j.aim.2024.109984","url":null,"abstract":"<div><div>Finding general conditions which ensure that a graph is Hamiltonian is a central topic in graph theory. An old and well-known conjecture in the area states that any <em>d</em>-regular <em>n</em>-vertex graph <em>G</em> whose second largest eigenvalue in absolute value <span><math><mi>λ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is at most <span><math><mi>d</mi><mo>/</mo><mi>C</mi></math></span>, for some universal constant <span><math><mi>C</mi><mo>></mo><mn>0</mn></math></span>, has a Hamilton cycle. In this paper, we obtain two main results which make substantial progress towards this problem. Firstly, we settle this conjecture in full when the degree <em>d</em> is at least a small power of <em>n</em>. Secondly, in the general case we show that <span><math><mi>λ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>d</mi><mo>/</mo><mi>C</mi><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></math></span> implies the existence of a Hamilton cycle, improving the 20-year old bound of <span><math><mi>d</mi><mo>/</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup><mo></mo><mi>n</mi></math></span> of Krivelevich and Sudakov. We use in a novel way a variety of methods, such as a robust Pósa rotation-extension technique, the Friedman-Pippenger tree embedding with rollbacks and the absorbing method, combined with additional tools and ideas.</div><div>Our results have several interesting applications. In particular, they imply the currently best-known bounds on the number of generators which guarantee the Hamiltonicity of random Cayley graphs, which is an important partial case of the well known Hamiltonicity conjecture of Lovász. They can also be used to improve a result of Alon and Bourgain on additive patterns in multiplicative subgroups.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109984"},"PeriodicalIF":1.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral invariants over the integers","authors":"Yusuke Kawamoto , Egor Shelukhin","doi":"10.1016/j.aim.2024.109976","DOIUrl":"10.1016/j.aim.2024.109976","url":null,"abstract":"<div><div>Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this setting which hold for <span><math><mi>Z</mi></math></span>-coefficients and fail for all field coefficients. For example, we prove that the spectral norm, an important metric derived from spectral invariants, is unbounded over <span><math><mi>Z</mi></math></span> for complex projective spaces, while it is uniformly bounded over all fields. This allows us to answer a symplectic version of a question of Hingston, originally asked in the setting of the energy functional on the loop space. We also provide applications to Hamiltonian dynamics and Hofer's geometry.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109976"},"PeriodicalIF":1.5,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Units of twisted group rings and their correlations to classical group rings","authors":"Geoffrey Janssens , Eric Jespers , Ofir Schnabel","doi":"10.1016/j.aim.2024.109983","DOIUrl":"10.1016/j.aim.2024.109983","url":null,"abstract":"<div><div>This paper is centred around the classical problem of extracting properties of a finite group <em>G</em> from the ring isomorphism class of its integral group ring <span><math><mi>Z</mi><mi>G</mi></math></span>. This problem is considered via describing the unit group <span><math><mi>U</mi><mo>(</mo><mi>Z</mi><mi>G</mi><mo>)</mo></math></span> generically for a finite group. Since the ‘90<em>s</em>’ several well known generic constructions of units are known to generate a subgroup of finite index in <span><math><mi>U</mi><mo>(</mo><mi>Z</mi><mi>G</mi><mo>)</mo></math></span> if <span><math><mi>Q</mi><mi>G</mi></math></span> does not have so-called exceptional simple epimorphic images, e.g. <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Q</mi><mo>)</mo></math></span>. However it remained a major open problem to find a <em>generic</em> construction under the presence of the latter type of simple images. In this article we obtain such generic construction of units. Moreover, this new construction also exhibits new properties, such as providing generically free subgroups of large rank. As an application we answer positively for several classes of groups recent conjectures on the rank and the periodic elements of the abelianisation <span><math><mi>U</mi><msup><mrow><mo>(</mo><mi>Z</mi><mi>G</mi><mo>)</mo></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msup></math></span>. To obtain all this, we investigate the group ring <em>R</em>Γ of an extension Γ of some normal subgroup <em>N</em> by a group <em>G</em>, over a domain <em>R</em>. More precisely, we obtain a direct sum decomposition of the (twisted) group algebra of Γ over the fraction field <em>F</em> of <em>R</em> in terms of various twisted group rings of <em>G</em> over finite extensions of <em>F</em>. Furthermore, concrete information on the kernel and cokernel of the associated projections is obtained. Along the way we also launch the investigations of the unit group of twisted group rings and of <span><math><mi>U</mi><mo>(</mo><mi>R</mi><mi>Γ</mi><mo>)</mo></math></span> via twisted group rings.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109983"},"PeriodicalIF":1.5,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Truncated pushforwards and refined unramified cohomology","authors":"Theodosis Alexandrou , Stefan Schreieder","doi":"10.1016/j.aim.2024.109979","DOIUrl":"10.1016/j.aim.2024.109979","url":null,"abstract":"<div><div>For a large class of cohomology theories, we prove that refined unramified cohomology is canonically isomorphic to the hypercohomology of a natural truncated complex of Zariski sheaves. This generalizes a classical result of Bloch and Ogus and solves a conjecture of Kok and Zhou.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109979"},"PeriodicalIF":1.5,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Frobenius representation type for invariant rings of finite groups","authors":"Mitsuyasu Hashimoto , Anurag K. Singh","doi":"10.1016/j.aim.2024.109978","DOIUrl":"10.1016/j.aim.2024.109978","url":null,"abstract":"<div><div>Let <em>V</em> be a finite rank vector space over a perfect field of characteristic <span><math><mi>p</mi><mo>></mo><mn>0</mn></math></span>, and let <em>G</em> be a finite subgroup of <span><math><mi>GL</mi><mo>(</mo><mi>V</mi><mo>)</mo></math></span>. If <em>V</em> is a permutation representation of <em>G</em>, or more generally a monomial representation, we prove that the ring of invariants <span><math><msup><mrow><mo>(</mo><mi>Sym</mi><mspace></mspace><mi>V</mi><mo>)</mo></mrow><mrow><mi>G</mi></mrow></msup></math></span> has finite Frobenius representation type. We also construct an example with <em>V</em> a finite rank vector space over the algebraic closure of the function field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, and <em>G</em> an elementary abelian subgroup of <span><math><mi>GL</mi><mo>(</mo><mi>V</mi><mo>)</mo></math></span>, such that the invariant ring <span><math><msup><mrow><mo>(</mo><mi>Sym</mi><mspace></mspace><mi>V</mi><mo>)</mo></mrow><mrow><mi>G</mi></mrow></msup></math></span> does not have finite Frobenius representation type.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109978"},"PeriodicalIF":1.5,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
