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Monatshefte für Mathematik最新文献

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Well-posedness of short time solutions and non-uniform dependence on the initial data for a shallow water wave model in critical Besov space 临界贝索夫空间浅水波浪模型的短时解的良好拟合性和对初始数据的非均匀依赖性
Monatshefte für Mathematik Pub Date : 2024-03-30 DOI: 10.1007/s00605-024-01959-x
Changtai Zhou, Honglin Xiao, Shaoyong Lai
{"title":"Well-posedness of short time solutions and non-uniform dependence on the initial data for a shallow water wave model in critical Besov space","authors":"Changtai Zhou, Honglin Xiao, Shaoyong Lai","doi":"10.1007/s00605-024-01959-x","DOIUrl":"https://doi.org/10.1007/s00605-024-01959-x","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140363619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On nonlocal Fokker–Planck equations with nonlinear force fields and perturbations 关于具有非线性力场和扰动的非局部福克-普朗克方程
Monatshefte für Mathematik Pub Date : 2024-03-30 DOI: 10.1007/s00605-024-01953-3
Tran Dinh Ke, Dao Trong Quyet, Dang Thi Phuong Thanh
{"title":"On nonlocal Fokker–Planck equations with nonlinear force fields and perturbations","authors":"Tran Dinh Ke, Dao Trong Quyet, Dang Thi Phuong Thanh","doi":"10.1007/s00605-024-01953-3","DOIUrl":"https://doi.org/10.1007/s00605-024-01953-3","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"32 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140362219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wave-breaking phenomena for a new weakly dissipative quasilinear shallow-water waves equation 一种新的弱耗散准线性浅水波方程的破浪现象
Monatshefte für Mathematik Pub Date : 2024-03-28 DOI: 10.1007/s00605-024-01958-y
Xiaofang Dong, Xianxian Su, Kai Wang
{"title":"Wave-breaking phenomena for a new weakly dissipative quasilinear shallow-water waves equation","authors":"Xiaofang Dong, Xianxian Su, Kai Wang","doi":"10.1007/s00605-024-01958-y","DOIUrl":"https://doi.org/10.1007/s00605-024-01958-y","url":null,"abstract":"<p>In this paper, we mainly study a new weakly dissipative quasilinear shallow-water waves equation, which can be formally derived from a model with the effect of underlying shear flow from the incompressible rotational two-dimensional shallow water in the moderately nonlinear regime by Wang, Kang and Liu (Appl Math Lett 124:107607, 2022). Considering the dissipative effect, the local well-posedness of the solution to this equation is first obtained by using Kato’s semigroup theory. We then establish the precise blow-up criterion by using the transport equation theory and Moser-type estimates. Moreover, some sufficient conditions which guarantee the occurrence of wave-breaking of solutions are studied according to the different real-valued intervals in which the dispersive parameter <span>(theta )</span> being located. It is noteworthy that we need to overcome the difficulty induced by complicated nonlocal nonlinear structure and different dispersive parameter ranges to get corresponding convolution estimates.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140322233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New results on spectral synthesis 光谱合成新成果
Monatshefte für Mathematik Pub Date : 2024-03-13 DOI: 10.1007/s00605-024-01950-6
László Székelyhidi
{"title":"New results on spectral synthesis","authors":"László Székelyhidi","doi":"10.1007/s00605-024-01950-6","DOIUrl":"https://doi.org/10.1007/s00605-024-01950-6","url":null,"abstract":"<p>In our former paper we introduced the concept of localization of ideals in the Fourier algebra of a locally compact Abelian group. It turns out that localizability of a closed ideal in the Fourier algebra is equivalent to the synthesizability of the annihilator of that closed ideal which corresponds to this ideal in the measure algebra. This equivalence provides an effective tool to prove synthesizability of varieties on locally compact Abelian groups. In this paper we utilize this tool to show that when investigating synthesizability of a variety, roughly speaking compact elements of the group can be neglected. Our main result is that spectral synthesis holds on a locally compact Abelian group <i>G</i> if and only if it holds on <i>G</i>/<i>B</i>, where <i>B</i> is the closed subgroup of all compact elements. In particular, spectral synthesis holds on compact Abelian groups. Also we obtain a simple proof for the characterization theorem of spectral synthesis on discrete Abelian groups.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions 兰金-塞尔伯格 L 函数的迪里希勒系数指数和
Monatshefte für Mathematik Pub Date : 2024-03-12 DOI: 10.1007/s00605-024-01952-4
Guangshi Lü, Qiang Ma
{"title":"Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions","authors":"Guangshi Lü, Qiang Ma","doi":"10.1007/s00605-024-01952-4","DOIUrl":"https://doi.org/10.1007/s00605-024-01952-4","url":null,"abstract":"<p>We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg <i>L</i>-functions attached to two cuspidal automorphic representations.\u0000</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a construction method of new moment sequences 关于新矩阵序列的构建方法
Monatshefte für Mathematik Pub Date : 2024-03-05 DOI: 10.1007/s00605-024-01947-1
Seunghwan Baek, Hayoung Choi, Seonguk Yoo
{"title":"On a construction method of new moment sequences","authors":"Seunghwan Baek, Hayoung Choi, Seonguk Yoo","doi":"10.1007/s00605-024-01947-1","DOIUrl":"https://doi.org/10.1007/s00605-024-01947-1","url":null,"abstract":"<p>In this paper we provide a way to construct new moment sequences from a given moment sequence. An operator based on multivariate positive polynomials is applied to get new moment sequences. A class of new sequences is corresponding to a unique symmetric polynomial; if this polynomial is positive, then the new sequence becomes again a moment sequence. We will see for instance that a new sequence generated from minors of a Hankel matrix of a Stieltjes moment sequence is also a Stieltjes moment sequence.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectrum of self-affine measures on the Sierpinski family 西尔平斯基族上的自阿芬度量谱
Monatshefte für Mathematik Pub Date : 2024-02-29 DOI: 10.1007/s00605-023-01939-7
{"title":"Spectrum of self-affine measures on the Sierpinski family","authors":"","doi":"10.1007/s00605-023-01939-7","DOIUrl":"https://doi.org/10.1007/s00605-023-01939-7","url":null,"abstract":"<h3>Abstract</h3> <p>In this study, a spectrum <span> <span>(Lambda )</span> </span> for the integral Sierpinski measures <span> <span>(mu _{M, D})</span> </span> with the digit set <span> <span>( D= left{ begin{pmatrix} 0 0 end{pmatrix}, begin{pmatrix} 1 0 end{pmatrix}, begin{pmatrix} 0 1 end{pmatrix}right} )</span> </span> is derived for a <span> <span>(2 times 2)</span> </span> diagonal matrix <em>M</em> with entries as <span> <span>(3ell _1)</span> </span> and <span> <span>(3ell _4)</span> </span> and for off-diagonal matrix <em>M</em> with both the off-diagonal entries as <span> <span>(3ell )</span> </span> where, <span> <span>(ell ,ell _1,ell _4 in {mathbb {Z}}{setminus }{{0}})</span> </span>. Additionally, the spectrum of <span> <span>(mu _{M, D})</span> </span> for a given <em>M</em> and a generalized digit set <em>D</em> is also examined. The spectrum of self-affine measures <span> <span>(mu _{M, D})</span> </span> on spatial Sierpinski gasket is obtained when <em>M</em> is diagonal matrix with entries <span> <span>(ell _i in 2{mathbb {Z}}setminus {{0}})</span> </span>, sign of <span> <span>(ell _i)</span> </span>’s are same and <span> <span>(D={0, e_1, e_2, e_3})</span> </span>, where <span> <span>(e_i's )</span> </span> are the standard basis in <span> <span>({mathbb {R}}^3)</span> </span>. Further, the spectrum of <span> <span>(mu _{M, D})</span> </span> for some off-diagonal <span> <span>(3times 3)</span> </span> matrices is also found. </p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
a-Weyl’s theorem and hypercyclicity 韦尔定理和超循环性
Monatshefte für Mathematik Pub Date : 2024-02-29 DOI: 10.1007/s00605-024-01951-5
Ying Liu, Xiaohong Cao
{"title":"a-Weyl’s theorem and hypercyclicity","authors":"Ying Liu, Xiaohong Cao","doi":"10.1007/s00605-024-01951-5","DOIUrl":"https://doi.org/10.1007/s00605-024-01951-5","url":null,"abstract":"<p>Let <i>H</i> be a complex infinite dimensional Hilbert space, <i>B</i>(<i>H</i>) be the algebra of all bounded linear operators acting on <i>H</i>, and <span>(overline{HC(H)})</span> <span>((overline{SC(H)}))</span> be the norm closure of the class of all hypercyclic operators (supercyclic operators) in <i>B</i>(<i>H</i>). An operator <span>(Tin B(H))</span> is said to be with hypercyclicity (supercyclicity) if <i>T</i> is in <span>(overline{HC(H)})</span> <span>((overline{SC(H)}))</span>. Using a new spectrum defined from “consistent in invertibility”, this paper gives necessary and sufficient conditions that <i>T</i> is with a-Browder’s theorem or with a-Weyl’s theorem. Further, this paper gives a necessary and sufficient condition that <i>T</i> is a-isoloid, with a-Weyl’s theorem and with hypercyclicity (supercyclicity) concurrently. Also, the relations between that <i>T</i> is with hypercyclicity (supercyclicity) and that <i>T</i> is both with a-Weyl’s theorem and a-isoloid are discussed by means of the new spectrum.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A refinement of the Hille–Wintner comparison theorem and new nonoscillation criteria for half-linear differential equations 希勒-温特纳比较定理的改进和半线性微分方程的新非振荡标准
Monatshefte für Mathematik Pub Date : 2024-02-21 DOI: 10.1007/s00605-024-01949-z
Jaroslav Jaroš
{"title":"A refinement of the Hille–Wintner comparison theorem and new nonoscillation criteria for half-linear differential equations","authors":"Jaroslav Jaroš","doi":"10.1007/s00605-024-01949-z","DOIUrl":"https://doi.org/10.1007/s00605-024-01949-z","url":null,"abstract":"<p>A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On polynomials in primes, ergodic averages and monothetic groups 论素数多项式、遍历平均数和单可数群
Monatshefte für Mathematik Pub Date : 2024-02-17 DOI: 10.1007/s00605-024-01948-0
Jaroslav Hančl, Radhakrishnan Nair, Jean-Louis Verger-Gaugry
{"title":"On polynomials in primes, ergodic averages and monothetic groups","authors":"Jaroslav Hančl, Radhakrishnan Nair, Jean-Louis Verger-Gaugry","doi":"10.1007/s00605-024-01948-0","DOIUrl":"https://doi.org/10.1007/s00605-024-01948-0","url":null,"abstract":"<p>Let <i>G</i> denote a compact monothetic group, and let <span>(rho (x) = alpha _k x^k + ldots + alpha _1 x + alpha _0)</span>, where <span>(alpha _0, ldots , alpha _k)</span> are elements of <i>G</i> one of which is a generator of <i>G</i>. Let <span>((p_n)_{nge 1})</span> denote the sequence of rational prime numbers. Suppose <span>(f in L^{p}(G))</span> for <span>(p&gt; 1)</span>. It is known that if </p><span>$$begin{aligned} A_{N}f(x):= {1 over N} sum _{n=1}^{N} f(x + rho (p_n)) quad (N=1,2, ldots ), end{aligned}$$</span><p>then the limit <span>(lim _{nrightarrow infty } A_Nf(x))</span> exists for almost all <i>x</i> with respect Haar measure. We show that if <i>G</i> is connected then the limit is <span>(int _{G} f dlambda )</span>. In the case where <i>G</i> is the <i>a</i>-adic integers, which is a totally disconnected group, the limit is described in terms of Fourier multipliers which are generalizations of Gauss sums.\u0000</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"211 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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