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A generalization of Lévy’s theorem on positive matrix semigroups 关于正矩阵半群的莱维定理的一般化
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-09-03 DOI: 10.1007/s10476-024-00039-4
M. Gerlach
{"title":"A generalization of Lévy’s theorem on positive matrix semigroups","authors":"M. Gerlach","doi":"10.1007/s10476-024-00039-4","DOIUrl":"https://doi.org/10.1007/s10476-024-00039-4","url":null,"abstract":"<p>We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero (“Lévy’s Theorem”). Our proof of this fact that does not require the matrices to be continuous at time zero. We also provide a formulation of this theorem in the terminology of positive operator semigroups on sequence spaces.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A $$(phi_frac{n}{s}, phi)$$ -Poincaré inequality on John domains 约翰域上的 $$(phi_frac{n}{s}, phi)$$ -Poincaré 不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-09-03 DOI: 10.1007/s10476-024-00038-5
S. Feng, T. Liang
{"title":"A $$(phi_frac{n}{s}, phi)$$ -Poincaré inequality on John domains","authors":"S. Feng, T. Liang","doi":"10.1007/s10476-024-00038-5","DOIUrl":"https://doi.org/10.1007/s10476-024-00038-5","url":null,"abstract":"<p>Let <span>(Omega)</span> be a bounded domain in <span>(mathbb{R}^n)</span> with <span>(nge2)</span> and <span>(sin(0,1))</span>. Assume that <span>(phi colon [0, infty) to [0, infty))</span> is a Young function obeying the doubling condition with the constant <span>(K_phi&lt; 2^{frac{n}{s}})</span>. We demonstrate that <span>(Omega)</span> supports a <span>((phi_frac{n}{s}, phi))</span>-Poincaré inequality if it is a John domain. Alternatively, assume further that <span>(Omega)</span> is a bounded domain that is quasiconformally equivalent to a uniform domain (for <span>(ngeq3)</span>) or a simply connected domain (for <span>(n=2)</span>), then we show that <span>(Omega)</span> is a John domain if a <span>((phi_frac{n}{s}, phi))</span>-Poincaré inequality holds.\u0000</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Generalized rectangular constant in Banach spaces 巴拿赫空间中的广义矩形常数
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-07-03 DOI: 10.1007/s10476-024-00034-9
H. Xie, Y. Fu, Y. Li
{"title":"Generalized rectangular constant in Banach spaces","authors":"H. Xie, Y. Fu, Y. Li","doi":"10.1007/s10476-024-00034-9","DOIUrl":"https://doi.org/10.1007/s10476-024-00034-9","url":null,"abstract":"<p>This paper presents two new geometric constants <span>(mu(X,a))</span> and <span>(mu'(X,a))</span>,\u0000which extend the rectangular constants <span>(mu(X))</span> and <span>(mu'(X))</span>. We firstly provide their bounds. Then the relationships between these geometric constants and the geometric properties of Banach spaces are discussed, including uniform nonsquareness, uniform convexity and uniform smoothness. Meanwhile, we provide several estimates of <span>(mu(l_p,a))</span> and obtain some new upper bound estimates on <span>(mu'(l_p,a))</span>.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A note on Maz'ya-Verbitsky capacitary inequalities 关于 Maz'ya-Verbitsky 容性不等式的说明
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-07-03 DOI: 10.1007/s10476-024-00037-6
K. H. Ooi
{"title":"A note on Maz'ya-Verbitsky capacitary inequalities","authors":"K. H. Ooi","doi":"10.1007/s10476-024-00037-6","DOIUrl":"https://doi.org/10.1007/s10476-024-00037-6","url":null,"abstract":"<p>We present a proof of Maz'ya-Verbitsky capacitary inequalities in terms of Bessel potentials. It will be seen that the proof mainly relies on the localization techniques. Several types of Kerman-Sawyer conditions will be obtained throughout the proof as well.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Perturbations of non-autonomous second-order abstract Cauchy problems 非自治二阶抽象柯西问题的扰动
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-07-01 DOI: 10.1007/s10476-024-00035-8
C. Budde, C. Seifert
{"title":"Perturbations of non-autonomous second-order abstract Cauchy problems","authors":"C. Budde, C. Seifert","doi":"10.1007/s10476-024-00035-8","DOIUrl":"https://doi.org/10.1007/s10476-024-00035-8","url":null,"abstract":"<p>In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract Cauchy problem in a product space, which we elaborate in full detail. As an application we provide a perturbed non-autonomous wave equation.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Difference analogues of the second main theorem for holomorphic curves and arbitrary families of hypersurfaces in projective varieties 全形曲线和投影面中任意超曲面族第二主定理的差分类似物
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-07-01 DOI: 10.1007/s10476-024-00036-7
T. B. Cao, N. V. Thin, S. D. Quang
{"title":"Difference analogues of the second main theorem for holomorphic curves and arbitrary families of hypersurfaces in projective varieties","authors":"T. B. Cao, N. V. Thin, S. D. Quang","doi":"10.1007/s10476-024-00036-7","DOIUrl":"https://doi.org/10.1007/s10476-024-00036-7","url":null,"abstract":"<p>Our goal in this paper is to establish some difference analogue of second main theorems for holomorphic curves into projective varieties intersecting arbitrary families of <i>c</i>-periodical hypersurfaces (fixed or moving) with truncated counting functions in various cases. Our results generalize and improve the previous results in this topic.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Non-spectral problem of self-affine measures with consecutive collinear digits in $$mathbb{R}^2$$ $$mathbb{R}^2$$中具有连续共线位数的自参量的非谱问题
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-06-18 DOI: 10.1007/s10476-024-00033-w
J. Su, S. Wu
{"title":"Non-spectral problem of self-affine measures with consecutive collinear digits in $$mathbb{R}^2$$","authors":"J. Su, S. Wu","doi":"10.1007/s10476-024-00033-w","DOIUrl":"https://doi.org/10.1007/s10476-024-00033-w","url":null,"abstract":"<p>Let <span>(mu_{M,D})</span> be the planar self-affine measure generated by an expanding integer matrix <span>(Min M_2(mathbb{Z}))</span> and an integer digit set <span>(D={0,1,dots,q-1}v)</span> with <span>(vinmathbb{Z}^2setminus{0})</span>, where <span>(gcd(det(M),q)=1)</span> and <span>(qge 2)</span> is an integer. If the characteristic polynomial of <span>(M)</span> is <span>(f(x)=x^2+det(M))</span> and <span>({v, Mv})</span> is linearly independent, we show that there exist at most <span>(q^2)</span> mutually orthogonal exponential functions in <span>(L^2(mu_{M,D}))</span>, and the number <span>(q^2)</span> is the best. In particular, we further give a complete description for the case <span>(M= {rm diag}(s, t))</span>\u0000with <span>(gcd(st, q)=1)</span>. This extends the results of Wei and Zhang [24].\u0000</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Old and new Morrey spaces without heat kernel bounds on RD-spaces RD 空间上无热核边界的新旧莫雷空间
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-06-18 DOI: 10.1007/s10476-024-00026-9
Bo Li, Ba. Li, B. Ma, A. Wang, J. Li
{"title":"Old and new Morrey spaces without heat kernel bounds on RD-spaces","authors":"Bo Li, Ba. Li, B. Ma, A. Wang, J. Li","doi":"10.1007/s10476-024-00026-9","DOIUrl":"https://doi.org/10.1007/s10476-024-00026-9","url":null,"abstract":"<p>An RD-space <span>(mathcal{X})</span> is a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse (volume) doubling condition.\u0000Let <span>(L)</span> be a non-negative self-adjoint operator acting on <span>(L^2(mathcal{X}))</span>.\u0000Assume that <span>(L)</span> generates an analytic semigroup <span>({mathrm{e}^{-tL}}_{t&gt;0})</span> whose kernels <span>({h_t(x,y)}_{t&gt;0})</span> satisfy a generalized Gaussian heat kernel upper estimate.\u0000Roughly speaking, the heat kernel behavior is a mixture of locally Gaussian and sub-Gaussian at infinity.\u0000With the help of this Gaussian heat kernel, we first introduce a novel Morrey space and then prove that it coincides with the classical Morrey space.\u0000As applications, some new characterizations of square Morrey space are established via a Carleson measure condition.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boundedness of some convolution-type operators on metric measure spaces 公度量空间上某些卷积型算子的有界性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-06-13 DOI: 10.1007/s10476-024-00030-z
J. M. Aldaz
{"title":"Boundedness of some convolution-type operators on metric measure spaces","authors":"J. M. Aldaz","doi":"10.1007/s10476-024-00030-z","DOIUrl":"https://doi.org/10.1007/s10476-024-00030-z","url":null,"abstract":"<p>We explore boundedness properties of some natural operators of\u0000convolution type in the context of metric measure spaces. Their study is suggested by certain transformations used in computer vision.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Dowker’s ergodic theorem by the Chacon–Ornstein theorem 通过查孔-奥恩斯坦定理的道克尔遍历定理
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-06-05 DOI: 10.1007/s10476-024-00032-x
M. Lin
{"title":"Dowker’s ergodic theorem by the Chacon–Ornstein theorem","authors":"M. Lin","doi":"10.1007/s10476-024-00032-x","DOIUrl":"https://doi.org/10.1007/s10476-024-00032-x","url":null,"abstract":"<p>We deduce Dowker’s general ratio ergodic theorem, and a vari-\u0000ant of it, from the Chacon–Ornstein theorem.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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