{"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}
{"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}
{"title":"Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges","authors":"Z. Douzi, B. Selmi, 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}
{"title":"On Meromorphic Solutions of Nonlinear Complex Differential Equations","authors":"J.-F. Chen, 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>∣ > ∣α<sub>2</sub>∣ > … > ∣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}
{"title":"On Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators","authors":"A. Ge, Q. He, 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>> <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}
{"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}
{"title":"On the Commutativity of Closed Symmetric Operators","authors":"S. Dehimi, M. H. Mortad, 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}
{"title":"Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G)","authors":"S. Soltani Renani, 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}
{"title":"Completion Procedures in Measure Theory","authors":"A. G. Smirnov, 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}
{"title":"Stability of ({cal A}{cal N})-Operators under Functional Calculus","authors":"G. Ramesh, H. Osaka, Y. Udagawa, 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}