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Stability of ANdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${cal A}{cal N}$$end{document}-Operators under Functi ANdocumentclass[12pt]｛minimum｝usepackage｛amsmath｝usepackage｛wasysym｝usepackup｛amsfonts｝usecpackage{amssymb｝usecpackage{amsbsy｝usecPackage｛mathrsfs｝usepackage{upgradeek｝setlength｛oddsedmargin｝｛-69pt｝ begin｛document｝$${document}-OperatorsFuncti
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-01 DOI: 10.1007/s10476-023-0231-5
G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki
{"title":"Stability of ANdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${cal A}{cal N}$$end{document}-Operators under Functi","authors":"G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki","doi":"10.1007/s10476-023-0231-5","DOIUrl":"https://doi.org/10.1007/s10476-023-0231-5","url":null,"abstract":"","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44656244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fermat and Malmquist type matrix differential equations 费马和马奎斯特型矩阵微分方程
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-06-08 DOI: 10.1007/s10476-023-0220-8
Y. X. Li, K. Liu, H. B. Si
{"title":"Fermat and Malmquist type matrix differential equations","authors":"Y. X. Li,&nbsp;K. Liu,&nbsp;H. B. Si","doi":"10.1007/s10476-023-0220-8","DOIUrl":"10.1007/s10476-023-0220-8","url":null,"abstract":"<div><p>The systems of nonlinear differential equations of certain types can be simplified to matrix forms. Two types of matrix differential equations will be considered in the paper, one is Fermat type matrix differential equation </p><div><div><span>$$A{(z)^n} + A'{(z)^n} = E$$</span></div></div><p> where <i>n</i> = 2 and <i>n</i> = 3, another is Malmquist type matrix differential equation </p><div><div><span>$$A'(z) = alpha A{(z)^2} + beta A(z) + gamma E,$$</span></div></div><p>, where <i>α</i> (≠ 0), <i>β, γ</i> are constants. By solving the systems of nonlinear differential equations, we obtain some properties on the meromorphic matrix solutions of the above matrix differential equations. In addition, we also consider two types of nonlinear differential equations, one of them is called Bi-Fermat differential equation.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43300318","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
Weyl’s asymptotic formula for fractal Laplacians defined by a class of self-similar measures with overlaps 由一类有重叠的自相似测度定义的分形拉普拉斯算子的Weyl渐近公式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-06-08 DOI: 10.1007/s10476-023-0222-6
W. Tang, Z. Y. Wang
{"title":"Weyl’s asymptotic formula for fractal Laplacians defined by a class of self-similar measures with overlaps","authors":"W. Tang,&nbsp;Z. Y. Wang","doi":"10.1007/s10476-023-0222-6","DOIUrl":"10.1007/s10476-023-0222-6","url":null,"abstract":"<div><p>We observe that some self-similar measures that we call essentially of finite type satisfy countable measure type condition. We make use of this condition to set up a framework to obtain a precise analog of Weyl’s asymptotic formula for the eigenvalue counting function of Laplacians defined by measures, emphasizing on one-dimensional self-similar measures with overlaps. As an application of our result, we obtain an analog of a semi-classical asymptotic formula for the number of negative eigenvalues of fractal Schrödinger operators as the parameter tends to infinity.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0222-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48110706","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
The gaussian convolution and reproducing kernels associated with the Hankel multidimensional operator 与Hankel多维算子相关的高斯卷积和再生核
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-06-08 DOI: 10.1007/s10476-023-0219-1
B. Amri
{"title":"The gaussian convolution and reproducing kernels associated with the Hankel multidimensional operator","authors":"B. Amri","doi":"10.1007/s10476-023-0219-1","DOIUrl":"10.1007/s10476-023-0219-1","url":null,"abstract":"<div><p>We consider the Hankel multidimensional operator defined on]0, +∞[<sup><i>n</i></sup> by </p><div><div><span>$${Delta _alpha} = sumlimits_{j = 1}^n {left({{{{partial ^2}} over {partial x_j^2}} + {{2{alpha _j} + 1} over {{x_j}}}{partial over {partial {x_j}}}} right)} $$</span></div></div><p> where <span>(alpha = ({alpha _1},{alpha _2}, ldots ,{alpha _n}) in ] - {1 over 2}, + infty {[^n})</span>. We give the most important harmonic analysis results related to the operator Δ<sub><i>α</i></sub> (translation operators <i>τ</i><sub><i>x</i></sub>, convolution product * and Hankel transform <i>ℌ</i><sub><i>α</i></sub>).</p><p>Using harmonic analysis results, we study spaces of Sobolev type for which we make explicit kernels reproducing. Next, we define and study the gaussian convolution <span>({{cal G}^t})</span>, <i>t</i> &gt; 0, associated with the Hankel multidimensinal operator Δ<sub><i>α</i></sub>. This transformation generalizes the classical gaussian transformation. We establish the most important properties of this transformation. In particular, we show that the gaussian transformation solves the heat equation, that is </p><div><div><span>$${Delta _alpha}(u)(x,t) = {{partial u} over {partial t}}(x,t),,,,,,(x,t) in [0, + infty {[^n} times ]0, + infty [.$$</span></div></div><p>In the second part of this work, we prove the existence and uniqueness of the extremal function associated with the gaussian transformation. We express this function using the reproducing kernels and we prove the important estimates for this extremal function.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44363619","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
Representing certain vector-valued function spaces as tensor products 将某些向量值函数空间表示为张量积
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-06-08 DOI: 10.1007/s10476-023-0218-2
M. Abtahi
{"title":"Representing certain vector-valued function spaces as tensor products","authors":"M. Abtahi","doi":"10.1007/s10476-023-0218-2","DOIUrl":"10.1007/s10476-023-0218-2","url":null,"abstract":"<div><p>Let <i>E</i> be a Banach space. For a topological space <i>X</i>, let <span>({{cal C}_b}(X,E))</span> be the space of all bounded continuous <i>E</i>-valued functions on <i>X</i>, and let <span>({{cal C}_K}(X,E))</span> be the subspace of <span>({{cal C}_b}(X,E))</span> consisting of all functions having a pre-compact image in <i>E</i>. We show that <span>({{cal C}_K}(X,E))</span> is isometrically isomorphic to the injective tensor product <span>({{cal C}_b}(X){{hat otimes}_varepsilon}E)</span>, and that <span>({{cal C}_b}(X,E) = {{cal C}_b}(X){{hat otimes}_varepsilon}E)</span> if and only if <i>E</i> is finite dimensional. Next, we consider the space Lip(<i>X, E</i>) of <i>E</i>-valued Lipschitz operators on a metric space (<i>X, d</i>) and its subspace Lip<sub><i>K</i></sub>(<i>X, E</i>) of Lipschitz compact operators. Utilizing the results on <span>({{cal C}_b}(X,E))</span>, we prove that Lip<sub><i>K</i></sub>(<i>X, E</i>) is isometrically isomorphic to a tensor product <span>({rm{Lip}}(X){{hat otimes}_alpha}E)</span>, and that <span>({rm{Lip}}(X,E) = {rm{Lip}}(X){{hat otimes}_alpha}E)</span> if and only if <i>E</i> is finite dimensional. Finally, we consider the space <i>D</i><sup>1</sup>(<i>X, E</i>) of continuously differentiable functions on a perfect compact plane set <i>X</i> and show that, under certain conditions, <i>D</i><sup>1</sup>(<i>X, E</i>) is isometrically isomorphic to a tensor product <span>({D^1}(X){hat otimes _beta}E)</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42413745","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
The pointwise James type constant 逐点James型常数
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-06-08 DOI: 10.1007/s10476-023-0221-7
M. A. Rincón-Villamizar
{"title":"The pointwise James type constant","authors":"M. A. Rincón-Villamizar","doi":"10.1007/s10476-023-0221-7","DOIUrl":"10.1007/s10476-023-0221-7","url":null,"abstract":"<div><p>In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all <i>x</i> ∈ <i>X</i>, ∥<i>x</i>∥ = 1, </p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div><p> We show that in almost transitive Banach spaces, the map <i>x</i> ∈ <i>X</i>, ∥<i>x</i>∥ = 1 ↦ <i>J</i>(<i>x, X, t</i>) is constant. As a consequence and having in mind the Mazur’s rotation problem, we prove that for almost transitive Banach spaces, the condition <span>(J(x,X,t) = sqrt 2 )</span> for some unit vector <i>x</i> ∈ <i>X</i> implies that <i>X</i> is Hilbert.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44497272","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
μ-Hankel operators on compact Abelian groups 紧阿贝尔群上的μ-Hankel算子
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-04-19 DOI: 10.1007/s10476-023-0217-3
A. Mirotin
{"title":"μ-Hankel operators on compact Abelian groups","authors":"A. Mirotin","doi":"10.1007/s10476-023-0217-3","DOIUrl":"10.1007/s10476-023-0217-3","url":null,"abstract":"<div><p>(<i>μ</i>; <i>ν</i>)-Hankel operators between separable Hilbert spaces were introduced and studied recently (A. Mirotin and E. Kuzmenkova, <i>μ</i>-Hankel operators on Hilbert spaces, Opuscula Math., 41 (2021), 881–899). This paper is devoted to generalization of (<i>μ; ν</i>)-Hankel operators to the case of (non-separable in general) Hardy spaces over compact and connected Abelian groups. In this setting bounded (<i>μ</i>; <i>ν</i>)-Hankel operators are fully described under some natural conditions. Examples of integral operators are also considered.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0217-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41736785","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
The pseudoinverse of the Laplacian matrix: Asymptotic behavior of its trace 拉普拉斯矩阵的伪逆：其迹的渐近性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-04-19 DOI: 10.1007/s10476-023-0216-4
F. Ecevit, C. Y. Yildirim
{"title":"The pseudoinverse of the Laplacian matrix: Asymptotic behavior of its trace","authors":"F. Ecevit,&nbsp;C. Y. Yildirim","doi":"10.1007/s10476-023-0216-4","DOIUrl":"10.1007/s10476-023-0216-4","url":null,"abstract":"<div><p>In this paper we are concerned with the asymptotic behavior of </p><div><div><span>$${rm{tr}}({cal L}_{{rm{sq}}}^ + ) = {1 over 4}sumlimits_{matrix{{j,k = 0} cr {(j,k) ne (0,0)} cr } }^{n - 1} {{1 over {1 - {1 over 2}(cos {{2pi j} over n} + cos {{2pi k} over n})}},} $$</span></div></div><p> the trace of the pseudoinverse of the Laplacian matrix related with the square lattice, as <i>n</i> → ∞. The method we developed for such sums in former papers depends on the use of Taylor approximations for the summands. It was shown that the error term depends on whether the Taylor polynomial used is of degree two or higher. Here we carry this out for the square lattice with a fourth degree Taylor polynomial and thereby obtain a result with an improved error term which is perhaps the most precise one can hope for.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48835438","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-archimedean Banach spaces of universal disposition 泛配置的非阿基米德Banach空间
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-03-31 DOI: 10.1007/s10476-023-0214-6
A. Kubzdela, C. Perez-Garcia
{"title":"Non-archimedean Banach spaces of universal disposition","authors":"A. Kubzdela,&nbsp;C. Perez-Garcia","doi":"10.1007/s10476-023-0214-6","DOIUrl":"10.1007/s10476-023-0214-6","url":null,"abstract":"<div><p>A space of universal disposition is a Banach space which has certain natural extension properties for isometric embeddings of Banach spaces belonging to a specific class. We study spaces of universal disposition for non-archimedean Banach spaces. In particular, we introduce the classification of non-archimedean Banach spaces depending on the cardinality of maximal orthogonal sets, which can be viewed as a kind of special density and characterize spaces of universal disposition for each distinguished class.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0214-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48770313","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
Poincaré inequalities on graphs 图上的Poincaré不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-03-31 DOI: 10.1007/s10476-023-0215-5
M. Levi, F. Santagati, A. Tabacco, M. Vallarino
{"title":"Poincaré inequalities on graphs","authors":"M. Levi,&nbsp;F. Santagati,&nbsp;A. Tabacco,&nbsp;M. Vallarino","doi":"10.1007/s10476-023-0215-5","DOIUrl":"10.1007/s10476-023-0215-5","url":null,"abstract":"<div><p>Every graph of bounded degree endowed with the counting measure satisfies a local version of <i>L</i><sup><i>p</i></sup>-Poincaré inequality, <i>p ∈</i> [1, ∞]. We show that on graphs which are trees the Poincaré constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of <i>L</i><sup><i>p</i></sup>-Poincaré inequality, despite the fact that they are nondoubling measures of exponential growth.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49050032","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: 2
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