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Weak Supercyclicity—An Expository Survey 弱超周期性--阐述性调查
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-05 DOI: 10.1007/s00025-024-02205-4
Carlos S. Kubrusly
{"title":"Weak Supercyclicity—An Expository Survey","authors":"Carlos S. Kubrusly","doi":"10.1007/s00025-024-02205-4","DOIUrl":"https://doi.org/10.1007/s00025-024-02205-4","url":null,"abstract":"<p>This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For operators on a normed space, the present paper explores the relationship among supercyclicity and three versions of weak supercyclicity, namely, weak l-sequential, weak sequential, and weak supercyclicities, and their connection with strong stability, weak stability, and weak quasistability. A survey of the literature on weak supercyclicity is followed by an analysis of the interplay between supercyclicity and strong stability, as well as between weak supercyclicity and weak stability. A description of the spectrum of weakly l-sequentially supercyclic operators is also given.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"24 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549883","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
On C-Normal Operator Matrices 关于 C 正态算子矩阵
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-05 DOI: 10.1007/s00025-024-02220-5
Eungil Ko, Ji Eun Lee, Mee-Jung Lee
{"title":"On C-Normal Operator Matrices","authors":"Eungil Ko, Ji Eun Lee, Mee-Jung Lee","doi":"10.1007/s00025-024-02220-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02220-5","url":null,"abstract":"<p>An operator <span>(Tin {mathcal {L(H)}})</span> is said to be <i>C-normal</i> if there exists a conjugation <i>C</i> on <span>({{mathcal {H}}})</span> such that the commutator <span>([(CT)^{#}, CT])</span> equals zero, where <span>([R,S]:=RS-SR)</span> and <span>(R^{#})</span> is a Hermitian adjont operator of <i>R</i> as in (1). If there exists a conjugation <i>C</i> with respect to which <span>(Tin mathcal {L(H)})</span> is <i>C</i>-normal, then <i>T</i> is called a <i>conjugation-normal</i> operator. In this paper, we study properties of conjugation-normal operator matrices. In particular, we focus on the conjugation-normality of the component operators of operator matrices which are conjugation-normal.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"35 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549884","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
Best Approximation and Inverse Results for Neural Network Operators 神经网络算子的最佳逼近和反演结果
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-22 DOI: 10.1007/s00025-024-02222-3
Lucian Coroianu, Danilo Costarelli
{"title":"Best Approximation and Inverse Results for Neural Network Operators","authors":"Lucian Coroianu, Danilo Costarelli","doi":"10.1007/s00025-024-02222-3","DOIUrl":"https://doi.org/10.1007/s00025-024-02222-3","url":null,"abstract":"<p>In the present paper we considered the problems of studying the best approximation order and inverse approximation theorems for families of neural network (NN) operators. Both the cases of classical and Kantorovich type NN operators have been considered. As a remarkable achievement, we provide a characterization of the well-known Lipschitz classes in terms of the order of approximation of the considered NN operators. The latter result has inspired a conjecture concerning the saturation order of the considered families of approximation operators. Finally, several noteworthy examples have been discussed in detail</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"13 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509407","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
Some Classes of Frontals and Its Representation Formulas 几类正面及其表示公式
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-16 DOI: 10.1007/s00025-024-02221-4
T. A. Medina-Tejeda
{"title":"Some Classes of Frontals and Its Representation Formulas","authors":"T. A. Medina-Tejeda","doi":"10.1007/s00025-024-02221-4","DOIUrl":"https://doi.org/10.1007/s00025-024-02221-4","url":null,"abstract":"<p>In this paper, we characterize the extendibility of the normal curvature at singularities of frontals and give a representation formula for the class of frontals with this property. We introduce the relative normal curvature, which allows us to study the classical normal curvature, the asymptotic curves and the lines of curvature through singularities. Also, we provide representation formulas for wavefronts near all types of singularities and subclasses, such as wavefronts with extendable Gaussian curvature, bounded Gaussian curvature, and extendable principal curvature, among others.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"293 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526725","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
Representations of Various Power Sums 各种幂和的表示方法
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-16 DOI: 10.1007/s00025-024-02190-8
Bikash Chakraborty, Raymond Mortini
{"title":"Representations of Various Power Sums","authors":"Bikash Chakraborty, Raymond Mortini","doi":"10.1007/s00025-024-02190-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02190-8","url":null,"abstract":"<p>We give new representations of various power sums, including the signed/alternating sum of powers of consecutive integers as well as odd numbers. The generalized Eulerian power sums <span>(E_{n,m}(z):=sum _{k=1}^n k^mz^k)</span> are also considered.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"174 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509408","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
Von Neumann Inequality and Dilation Theory on Regular $${{mathcal {U}}}$$ -Twisted Polyballs 正规 $${{mathcal {U}}}$ 扭转多球上的冯-诺依曼不等式和膨胀理论
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-16 DOI: 10.1007/s00025-024-02218-z
Gelu Popescu
{"title":"Von Neumann Inequality and Dilation Theory on Regular $${{mathcal {U}}}$$ -Twisted Polyballs","authors":"Gelu Popescu","doi":"10.1007/s00025-024-02218-z","DOIUrl":"https://doi.org/10.1007/s00025-024-02218-z","url":null,"abstract":"<p>The goal of this paper is to develop a dilation theory on the regular <span>({{mathcal {U}}})</span>-twisted polyball <span>(textbf{B}_{{mathcal {U}}}({{mathcal {H}}}))</span>, which is the set of all <i>k</i>-tuples <span>(T:=(T_1,ldots , T_k))</span> of row contractions <span>(T_i:=[T_{i,1}cdots T_{i,n_i}])</span> on a Hilbert space <span>({{mathcal {H}}})</span> satisfying certain positivity condition on the defect operator <span>(Delta _T(I))</span> and <span>({{mathcal {U}}})</span>-commutation relations, where <span>({{mathcal {U}}}subset B({{mathcal {H}}}))</span> is an appropriate set of unitary operators. The role of operator model is played by a standard multi-shift <span>(textbf{S}:=(textbf{S}_1,ldots , textbf{S}_k))</span> with <span>(textbf{S}_i:=[textbf{S}_{i,1}cdots textbf{S}_{i,n_i}])</span>, which is a <i>k</i>-tuple of doubly <span>(Iotimes {{mathcal {U}}})</span>-commuting pure row isometries on the Hilbert space <span>(ell ^2({{mathbb {F}}}_{n_1}^+times cdots times {{mathbb {F}}}_{n_k}^+)otimes {{mathcal {H}}})</span>, where <span>({{mathbb {F}}}_{n_i}^+)</span> is the unital free semigroup with <span>(n_i)</span> generators and each <span>(textbf{S}_{i,j})</span> is a weighted shift with operator-valued weights. It is shown that many of the classical results concerning the dilation theory of contractions on Hilbert spaces have analogues for <span>({{mathcal {U}}})</span>-twisted polyballs. This includes: Sz.-Nagy dilation theorem, von Neumann inequality, Itô and Brehmer dilations for commuting isometries and contractions, respectively, and Beurling characterization of the invariant subspaces for the unilateral shift on the Hardy space <span>(H^2)</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"86 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552900","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
Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces 革命曲面上曲线缩短流的旋转孤子
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-16 DOI: 10.1007/s00025-024-02219-y
B. Leandro, R. Novais, H. Reis
{"title":"Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces","authors":"B. Leandro, R. Novais, H. Reis","doi":"10.1007/s00025-024-02219-y","DOIUrl":"https://doi.org/10.1007/s00025-024-02219-y","url":null,"abstract":"<p>We present a characterization for the rotational soliton for the curve shortening flow (CSF) on the revolution surfaces of <span>(mathbb {R}^3)</span>. Furthermore, we describe the behavior of such curves by showing that the two ends of each open curve are asymptotic to a parallel geodesic.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"7 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532470","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
Invariant measures from locally bounded orbits 来自局部有界轨道的不变度量
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-15 DOI: 10.1007/s00025-024-02204-5
Antoni López-Martínez
{"title":"Invariant measures from locally bounded orbits","authors":"Antoni López-Martínez","doi":"10.1007/s00025-024-02204-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02204-5","url":null,"abstract":"<p>Motivated by recent investigations of Sophie Grivaux and Étienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of <i>locally bounded orbit</i> for a continuous linear operator <span>(T:Xlongrightarrow X)</span> acting on a Fréchet space <i>X</i>, and we use this new notion to construct (non-trivial) <i>T</i>-invariant probability Borel measures on <span>((X,mathscr {B}(X)))</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"86 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526726","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
On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes with State-Dependent Jump Intensity 论具有状态相关跃迁强度的某些片断确定性马尔可夫过程的静态分布的存在性和唯一性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-14 DOI: 10.1007/s00025-024-02195-3
Dawid Czapla
{"title":"On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes with State-Dependent Jump Intensity","authors":"Dawid Czapla","doi":"10.1007/s00025-024-02195-3","DOIUrl":"https://doi.org/10.1007/s00025-024-02195-3","url":null,"abstract":"<p>In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which the trajectory is driven by one of the given semiflows. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the Markov chains given by their post-jump locations. Using this result, we further establish a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of a random iterated function system with an arbitrary set of transformations.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"22 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532216","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
On Multi-step Extended Maximum Residual Kaczmarz Method for Solving Large Inconsistent Linear Systems 论求解大型不一致线性系统的多步扩展最大残差 Kaczmarz 法
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-06-14 DOI: 10.1007/s00025-024-02210-7
A.-Qin Xiao, Jun-Feng Yin, Ning Zheng
{"title":"On Multi-step Extended Maximum Residual Kaczmarz Method for Solving Large Inconsistent Linear Systems","authors":"A.-Qin Xiao, Jun-Feng Yin, Ning Zheng","doi":"10.1007/s00025-024-02210-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02210-7","url":null,"abstract":"<p>A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"74 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526727","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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