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Kolmogorov and Markov Type Inequalities on Certain Algebraic Varieties 若干代数变种上的Kolmogorov和Markov型不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0224-4
T. Beberok
{"title":"Kolmogorov and Markov Type Inequalities on Certain Algebraic Varieties","authors":"T. Beberok","doi":"10.1007/s10476-023-0224-4","DOIUrl":"10.1007/s10476-023-0224-4","url":null,"abstract":"<div><p>In this paper we introduce a generalization to compact subsets of certain algebraic varieties of the classical Markov inequality on the derivatives of a polynomial in terms of its own values. We also introduce an extension to such sets of a local form of the classical Markov inequality, and show the equivalence of introduced Markov and local Markov inequalities.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"681 - 697"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45005511","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
Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density 具有有界密度谱的欧氏空间上的傅立叶拟晶及其分布
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0228-0
S. Yu. Favorov
{"title":"Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density","authors":"S. Yu. Favorov","doi":"10.1007/s10476-023-0228-0","DOIUrl":"10.1007/s10476-023-0228-0","url":null,"abstract":"<div><p>We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sums of derivatives of generalized lattice Dirac combs. These theorems are derived from properties of families of discretely supported measures and almost periodic distributions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"747 - 764"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0228-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49043400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges 关于二重规的Hewitt-Stromberg测度的一些正则性质
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0227-1
Z. Douzi, B. Selmi, Z. Yuan
{"title":"Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges","authors":"Z. Douzi,&nbsp;B. Selmi,&nbsp;Z. Yuan","doi":"10.1007/s10476-023-0227-1","DOIUrl":"10.1007/s10476-023-0227-1","url":null,"abstract":"<div><p>The aim of this paper is to show that if the Hewitt–Stromberg pre-measures with respect to the gauge are finite, then these pre-measures have a kind of <i>outer regularity</i> in a general metric space <i>X</i>. We give also some conditions on the Hewitt–Stromberg pre-measures with respect to the gauge such that the Hewitt–Stromberg measures have an almost <i>inner regularity</i> on a complete separable metric space <i>X</i>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"733 - 746"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45161713","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 Meromorphic Solutions of Nonlinear Complex Differential Equations 关于非线性复微分方程的亚纯解
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0225-3
J.-F. Chen, Y.-Y. Feng
{"title":"On Meromorphic Solutions of Nonlinear Complex Differential Equations","authors":"J.-F. Chen,&nbsp;Y.-Y. Feng","doi":"10.1007/s10476-023-0225-3","DOIUrl":"10.1007/s10476-023-0225-3","url":null,"abstract":"<div><p>By utilizing Nevanlinna theory of meromorphic functions, we characterize meromorphic solutions of the following nonlinear differential equation of the form </p><div><div><span>$${f^n}{f^prime } + P(z,f,{f^prime }, ldots ,{f^{(t)}}) = {P_1}{e^{{alpha _1}z}} + {P_2}{e^{{alpha _2}z}} + cdots + {P_m}{e^{{alpha _m}z}},$$</span></div></div><p> where <i>n</i> ≥ 3, <i>t</i> ≥ 0 and <i>m</i> ≥ 1 are integers, <i>n</i> ≥ <i>m, P</i>(<i>z, f, f′, …, f</i><sup>(<i>t</i>)</sup>) is a differential polynomial in <i>f</i> (<i>z</i>) of degree <i>d</i> ≤ <i>n</i> with small functions of <i>f</i> (<i>z</i>) as its coefficients, and α<sub><i>j</i></sub>, <i>P</i><sub><i>j</i></sub> (<i>j</i> = 1, 2, …, <i>m</i>) are nonzero constants such that ∣α<sub>1</sub>∣ &gt; ∣α<sub>2</sub>∣ &gt; … &gt; ∣α<sub><i>m</i></sub>∣. Also we provide the concrete forms of the solutions of the equation above, and present some examples illustrating the sharpness of our results.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"699 - 719"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0225-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41583690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators 关于与Schrödinger算子相关的换向子振荡和变分的加权紧性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0229-z
A. Ge, Q. He, D. Yan
{"title":"On Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators","authors":"A. Ge,&nbsp;Q. He,&nbsp;D. Yan","doi":"10.1007/s10476-023-0229-z","DOIUrl":"10.1007/s10476-023-0229-z","url":null,"abstract":"<div><p>Let <span>({cal L} = - Delta + V)</span> be a Schrödinger operator with a nonnegative potential <i>V</i> belonging to the reverse Hölder class <i>B</i><sub><i>q</i></sub> for <i>q</i>&gt; <i>n</i>/2. In this paper, we study the weighted compactness of oscillation and variation commutators generated by BMO-type functions and some Schrödinger operators, which include Riesz transform and other standard Calderón–Zygmund operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"765 - 805"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0229-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41861009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps 向量值可微映射空间的Banach-Stone型定理
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0232-4
A. Ranjbar-Motlagh
{"title":"A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps","authors":"A. Ranjbar-Motlagh","doi":"10.1007/s10476-023-0232-4","DOIUrl":"10.1007/s10476-023-0232-4","url":null,"abstract":"<div><p>This article describes the surjective linear isometries between spaces of <i>p</i>-times differentiable maps from a domain of the Euclidean space into a certain Banach space.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"841 - 854"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44727164","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 Commutativity of Closed Symmetric Operators 关于闭对称算子的交换性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0226-2
S. Dehimi, M. H. Mortad, A. Bachir
{"title":"On the Commutativity of Closed Symmetric Operators","authors":"S. Dehimi,&nbsp;M. H. Mortad,&nbsp;A. Bachir","doi":"10.1007/s10476-023-0226-2","DOIUrl":"10.1007/s10476-023-0226-2","url":null,"abstract":"<div><p>In this paper, we mainly show that if a product <i>AB</i> (or <i>BA</i>) of a closed symmetric operator <i>A</i> and a bounded positive operator <i>B</i> is normal, then it is self-adjoint. Equivalently, this means that <i>B</i> commutes with <i>A</i>. Certain generalizations and consequences are also presented.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"721 - 731"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43472144","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
Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G) 群代数上某些Banach右模的射影性ℓ1（G）
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0234-2
S. Soltani Renani, Z. Yari
{"title":"Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G)","authors":"S. Soltani Renani,&nbsp;Z. Yari","doi":"10.1007/s10476-023-0234-2","DOIUrl":"10.1007/s10476-023-0234-2","url":null,"abstract":"<div><p>Let <i>G</i> be a locally compact group, <span>({cal B}({L^2}(G)))</span> be the space of all bounded linear operators on <i>L</i><sup>2</sup>(<i>G</i>), and <span>(({cal T}({L^2}(G)), ast))</span> be the Banach algebra of trace class operators on <i>L</i><sup>2</sup>(<i>G</i>). In this paper, we focus on some Banach right submodules of <span>({cal B}({L^2}(G)))</span> over the convolution algebras <span>(({cal T}({L^2}(G)), ast))</span> and (<i>L</i><sup>1</sup>(<i>G</i>),*). We will see that if the locally compact group <i>G</i> is discrete, then the Banach right <i>ℓ</i><sup>1</sup>(<i>G</i>)-module structures of them are derived from their Banach right <span>({cal T}({ell ^2}(G)))</span>-module structures. We also study the projectivity of these Banach right <i>ℓ</i><sup>1</sup>(<i>G</i>)-modules.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"881 - 890"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46322216","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
Completion Procedures in Measure Theory 测量理论中的完成程序
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0233-3
A. G. Smirnov, M. S. Smirnov
{"title":"Completion Procedures in Measure Theory","authors":"A. G. Smirnov,&nbsp;M. S. Smirnov","doi":"10.1007/s10476-023-0233-3","DOIUrl":"10.1007/s10476-023-0233-3","url":null,"abstract":"<div><p>We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content <i>μ</i>. With every such ring <span>({cal N})</span>, an extension of <i>μ</i> is naturally associated which is called the <span>({cal N})</span>-completion of <i>μ</i>. The <span>({cal N})</span>-completion operation comprises most previously known completion-type procedures and also gives rise to some new extensions, which may be useful for constructing counterexamples in measure theory. We find a condition ensuring that <i>σ</i>-additivity of a content is preserved under the <span>({cal N})</span>-completion and establish a criterion for the <span>({cal N})</span>-completion of a measure to be again a measure.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"855 - 880"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42483533","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
Stability of ({cal A}{cal N})-Operators under Functional Calculus 函数微积分下（｛cal A｝｛cl N｝）-算子的稳定性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0231-5
G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki
{"title":"Stability of ({cal A}{cal N})-Operators under Functional Calculus","authors":"G. Ramesh,&nbsp;H. Osaka,&nbsp;Y. Udagawa,&nbsp;T. Yamazaki","doi":"10.1007/s10476-023-0231-5","DOIUrl":"10.1007/s10476-023-0231-5","url":null,"abstract":"<div><p>In this note we discuss absolutely norm attaining property (<span>({cal A}{cal N})</span>-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the <span>({cal A}{cal N})</span>-property under the functional calculus. As a consequence we discuss the operator mean of positive <span>({cal A}{cal N})</span>-operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"825 - 839"},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0231-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50431404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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