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Maximum principles and direct methods for tempered fractional operators 有节制分数算子的最大原则和直接方法
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2639-4
Yuxia Guo, Shaolong Peng
{"title":"Maximum principles and direct methods for tempered fractional operators","authors":"Yuxia Guo, Shaolong Peng","doi":"10.1007/s11856-024-2639-4","DOIUrl":"https://doi.org/10.1007/s11856-024-2639-4","url":null,"abstract":"<p>In this paper, we are concerned with the tempered fractional operator <span>(-(Delta+lambda)^{alphaover{2}})</span> with <i>α</i> ∈ (0, 2) and λ is a sufficiently small positive constant. We first establish various maximum principle principles and develop the direct moving planes and sliding methods for anti-symmetric functions involving tempered fractional operators. And then we consider tempered fractional problems. As applications, we extend the direct method of moving planes and sliding methods for the tempered fractional problem, and discuss how they can be used to establish symmetry, monotonicity, Liouville-type results and uniqueness results for solutions in various domains. We believe that our theory and methods can be conveniently applied to study other problems involving tempered fractional operators.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938641","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
Small deviation estimates and small ball probabilities for geodesics in last passage percolation 最后通道渗流中大地线的小偏差估计和小球概率
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2635-8
Riddhipratim Basu, Manan Bhatia
{"title":"Small deviation estimates and small ball probabilities for geodesics in last passage percolation","authors":"Riddhipratim Basu, Manan Bhatia","doi":"10.1007/s11856-024-2635-8","DOIUrl":"https://doi.org/10.1007/s11856-024-2635-8","url":null,"abstract":"<p>For the exactly solvable model of exponential last passage percolation on ℤ<sup>2</sup>, consider the geodesic Γ<sub><i>n</i></sub> joining (0, 0) and (<i>n, n</i>) for large <i>n</i>. It is well known that the transversal fluctuation of Γ<sub><i>n</i></sub> around the line <i>x</i> = <i>y</i> is <i>n</i><sup>2/3+<i>o</i>(1)</sup> with high probability. We obtain the exponent governing the decay of the small ball probability for Γ<sub><i>n</i></sub> and establish that for small <i>δ</i>, the probability that Γ<sub><i>n</i></sub> is contained in a strip of width <i>δn</i><sup>2/3</sup> around the diagonal is exp(−Θ(<i>δ</i><sup>−3/2</sup>)) uniformly in high <i>n</i>. We also obtain optimal small deviation estimates for the one point distribution of the geodesic showing that for <span>({t}over{2n})</span> bounded away from 0 and 1, we have ℙ(∣<i>x</i>(<i>t</i>) − <i>y</i>(<i>t</i>)∣ ≤ <i>δn</i><sup>2/3</sup>) = Θ(<i>δ</i>) uniformly in high <i>n</i>, where (<i>x</i>(<i>t</i>), <i>y</i>(<i>t</i>)) is the unique point where Γ<sub><i>n</i></sub> intersects the line <i>x</i> + <i>y</i> = <i>t</i>. Our methods are expected to go through for other exactly solvable models of planar last passage percolation and also, upon taking the <i>n</i> → ∞ limit, expected to provide analogous estimates for geodesics in the directed landscape.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938646","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
Effective bounds for the decay of Schrödinger eigenfunctions and Agmon bubbles 薛定谔特征函数衰变和阿格蒙气泡的有效边界
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2641-x
Stefan Steinerberger
{"title":"Effective bounds for the decay of Schrödinger eigenfunctions and Agmon bubbles","authors":"Stefan Steinerberger","doi":"10.1007/s11856-024-2641-x","DOIUrl":"https://doi.org/10.1007/s11856-024-2641-x","url":null,"abstract":"<p>We study solutions of −Δ<i>u</i> + <i>Vu</i> = λ<i>u</i> on ℝ<sup><i>n</i></sup>. Such solutions localize in the ‘allowed’ region {<i>x</i> ∈ ℝ<sup><i>n</i></sup>: <i>V</i>(<i>x</i>) ≤ λ} and decay exponentially in the ‘forbidden’ region {<i>x</i> ∈ ℝ<sup><i>n</i></sup>: <i>V</i>(<i>x</i>) &gt; λ}. One way of making this precise is Agmon’s inequality implying decay estimates in terms of the Agmon metric. We prove a complementary decay estimate in terms of harmonic measure which can improve on Agmon’s estimate, connect the Agmon metric to decay of harmonic measure and prove a sharp pointwise Agmon estimate.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938643","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
Simplified presentations and embeddings of Demazure modules Demazure 模块的简化展示和嵌入
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2652-7
Deniz Kus, Rajendran Venkatesh
{"title":"Simplified presentations and embeddings of Demazure modules","authors":"Deniz Kus, Rajendran Venkatesh","doi":"10.1007/s11856-024-2652-7","DOIUrl":"https://doi.org/10.1007/s11856-024-2652-7","url":null,"abstract":"<p>For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g., level one in type A) which becomes in the limit (for anti-dominant weights) the well-known embedding of finite-dimensional irreducible modules of the underlying simple Lie algebra into the tensor product of fundamental modules. To achieve this goal, we first simplify the presentation of these modules extending the results of [13] in the <span>({mathfrak g})</span>-stable case. As an application, we propose a crystal theoretic way to find classical decompositions with respect to a maximal semi-simple Lie subalgebra by identifying the Demazure crystal as a connected component in the corresponding tensor product of crystals.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221611","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
The P-ideal dichotomy, Martin’s axiom and entangled sets P-理想二分法、马丁公理和纠缠集
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2651-8
Osvaldo Guzmán, Stevo Todorcevic
{"title":"The P-ideal dichotomy, Martin’s axiom and entangled sets","authors":"Osvaldo Guzmán, Stevo Todorcevic","doi":"10.1007/s11856-024-2651-8","DOIUrl":"https://doi.org/10.1007/s11856-024-2651-8","url":null,"abstract":"<p>We build a model of the <i>P</i>-ideal ichotomy (PID) and Martin’s axiom for <i>ω</i><sub>1</sub> (<span>({rm MA}_{{omega}_1})</span>) in which there is a 2-entangled set of reals. In particular, it follows that the Open Graph Axiom or Baumgartner’s axiom for <i>ω</i><sub>1</sub>-dense sets are not consequences of <span>({rm PID} + {rm MA}_{{omega}_1})</span>. We review Neeman’s iteration method using two type side conditions and provide an alternative proof for the preservation of properness.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221371","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
New central elements in free alternative algebras 自由替代代数中的新中心元
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2650-9
Ivan Shestakov, Sergei Sverchkov
{"title":"New central elements in free alternative algebras","authors":"Ivan Shestakov, Sergei Sverchkov","doi":"10.1007/s11856-024-2650-9","DOIUrl":"https://doi.org/10.1007/s11856-024-2650-9","url":null,"abstract":"<p>A new series of central elements is found in the free alternative algebra. More exactly, let Alt[<i>X</i>] and SMalc[<i>X</i>] ⊂ Alt[<i>X</i>] be the free alternative algebra and the free special Malcev algebra over a field of characteristic 0 on a set of free generators <i>X</i>, and let <i>f</i> (<i>x, y, x</i><sub>1</sub>,…, <i>x</i><sub><i>n</i></sub>) ∈ SMalc[<i>X</i>] be a multilinear element which is trivial in the free associative algebra. Then the element <i>u</i><sub><i>n</i></sub> = <i>u</i><sub><i>n</i></sub> (<i>x, x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>) = <i>f</i> (<i>x</i><sup>2</sup>, <i>x, x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>) − <i>f</i> (<i>x, x</i><sup>2</sup>,<i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>) lies in the center of the algebra Alt[<i>X</i>]. The elements <i>u</i><sub><i>n</i></sub>(<i>x, x</i><sub>1</sub>,…, <i>x</i><sub><i>n</i></sub>) are uniquely defined up to a scalar for a given <i>n</i> (that is, they do not depend on <i>f</i> but only on deg <i>f</i>), and they are skew-symmetric on the variables <i>x</i><sub>1</sub>,…,<i>x</i><sub><i>n</i></sub>. Moreover, <i>u</i><sub><i>n</i></sub> = 0 for <i>n</i> = 4<i>m</i> + 2, 4<i>m</i> + 3 and <i>u</i><sub><i>n</i></sub> ≠ 0 for <i>n</i> = 4<i>m</i>, 4<i>m</i> + 1. The ideals generated by the elements <i>u</i><sub>4<i>m</i></sub>, <i>u</i><sub>4<i>m</i>+1</sub> lie in the associative center of the algebra Alt[<i>X</i>] and have trivial multiplication.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221369","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
Continuity properties of folding entropy 折叠熵的连续性
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2653-6
Gang Liao, Shirou Wang
{"title":"Continuity properties of folding entropy","authors":"Gang Liao, Shirou Wang","doi":"10.1007/s11856-024-2653-6","DOIUrl":"https://doi.org/10.1007/s11856-024-2653-6","url":null,"abstract":"<p>The folding entropy is a quantity originally proposed by Ruelle in 1996 during the study of entropy production in the non-equilibrium statistical mechanics [53]. As derived through a limiting process to the non-equilibrium steady state, the continuity of entropy production plays a key role in its physical interpretations. In this paper, the continuity of folding entropy is studied for a general (non-invertible) differentiable dynamical system with degeneracy. By introducing a notion called degenerate rate, it is proved that on any subset of measures with uniform degenerate rate, the folding entropy, and hence the entropy production, is upper semi-continuous. This extends the upper semi-continuity result in [53] from endomorphisms to all <i>C</i><sup><i>r</i></sup> (<i>r</i> &gt; 1) maps.</p><p>We further apply our result in the one-dimensional setting. In achieving this, an equality between the folding entropy and (Kolmogorov–Sinai) metric entropy, as well as a general dimension formula are established. The upper semi-continuity of metric entropy and dimension are then valid when measures with uniform degenerate rate are considered. Moreover, the sharpness of the uniform degenerate rate condition is shown by examples of <i>C</i><sup><i>r</i></sup> interval maps with positive metric (and folding) entropy.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221608","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
Distinguishing sets of strong recurrence from van der Corput sets 区分强递归集和范德科普特集
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2644-7
Andreas Mountakis
{"title":"Distinguishing sets of strong recurrence from van der Corput sets","authors":"Andreas Mountakis","doi":"10.1007/s11856-024-2644-7","DOIUrl":"https://doi.org/10.1007/s11856-024-2644-7","url":null,"abstract":"<p>Sets of recurrence, which were introduced by Furstenberg, and van der Corput sets, which were introduced by Kamae and Mendés France, as well as variants thereof, are important classes of sets in Ergodic Theory. In this paper, we construct a set of strong recurrence which is not a van der Corput set. In particular, this shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. This answers some questions asked by Bergelson and Lesigne.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221368","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
Complements of discriminants of simple real function singularities 简单实函数奇点的判别式补集
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2627-8
Victor A. Vassiliev
{"title":"Complements of discriminants of simple real function singularities","authors":"Victor A. Vassiliev","doi":"10.1007/s11856-024-2627-8","DOIUrl":"https://doi.org/10.1007/s11856-024-2627-8","url":null,"abstract":"<p>All components of complements of discriminant varieties of simple real function singularities are explicitly listed. A combinatorial algorithm enumerating the topological types of morsifications of real function singularities is promoted.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938644","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
Stability and deformation of F-singularities Fingularities 的稳定性和变形
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2024-08-04 DOI: 10.1007/s11856-024-2638-5
Alessandro De Stefani, Ilya Smirnov
{"title":"Stability and deformation of F-singularities","authors":"Alessandro De Stefani, Ilya Smirnov","doi":"10.1007/s11856-024-2638-5","DOIUrl":"https://doi.org/10.1007/s11856-024-2638-5","url":null,"abstract":"<p>We study the problem of m-adic stability of <i>F</i>-singularities, that is, whether the property that a quotient of a local ring (<span>(R,mathfrak{m})</span>) by a non-zero divisor <span>(xinmathfrak{m})</span> has good <i>F</i>-singularities is preserved in a sufficiently small <span>(mathfrak{m})</span>-adic neighborhood of <i>x</i>. We show that <span>(mathfrak{m})</span>-adic stability holds for <i>F</i>-rationality in full generality, and for <i>F</i>-injectivity, <i>F</i>-purity and strong <i>F</i>-regularity under certain assumptions. We show that strong <i>F</i>-regularity and <i>F</i>-purity are not stable in general. Moreover, we exhibit strong connections between stability and deformation phenomena, which hold in great generality.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938642","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
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