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Asymptotically uniform functions: a single hypothesis which solves two old problems 渐近均匀函数：一个假设解决两个老问题
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-05 DOI: 10.1007/s10476-024-00024-x
J.-P. Gabriel, J.-P. Berrut
{"title":"Asymptotically uniform functions: a single hypothesis which solves two old problems","authors":"J.-P. Gabriel,&nbsp;J.-P. Berrut","doi":"10.1007/s10476-024-00024-x","DOIUrl":"10.1007/s10476-024-00024-x","url":null,"abstract":"<div><p>The asymptotic study of a time-dependent function ƒ as the solution of a differential equation often leads to the question of whether its derivative <span>(f')</span> vanishes at infinity. We show that a necessary and sufficient condition for this is that <span>(f')</span> is what may be called asymptotically uniform. We generalize the result to higher order derivatives. We also show that the same property for ƒ itself is also necessary and sufficient for its one-sided improper integrals to exist. The article provides a broad study of such asymptotically uniform functions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00024-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253379","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 crystalline measure that is not a Fourier quasicrystal 不属于傅立叶准晶体的晶体量
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s10476-024-00031-y
S. Yu. Favorov
{"title":"A crystalline measure that is not a Fourier quasicrystal","authors":"S. Yu. Favorov","doi":"10.1007/s10476-024-00031-y","DOIUrl":"10.1007/s10476-024-00031-y","url":null,"abstract":"<div><p>We construct a crystalline measure on the real line that is not a\u0000Fourier quasicrystal.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00031-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253100","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 universal formula for derivation operators and applications 推导算子的通用公式及其应用
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-06-03 DOI: 10.1007/s10476-024-00028-7
J. Suárez de la Fuente
{"title":"A universal formula for derivation operators and applications","authors":"J. Suárez de la Fuente","doi":"10.1007/s10476-024-00028-7","DOIUrl":"10.1007/s10476-024-00028-7","url":null,"abstract":"<div><p>We give a universal formula describing derivation operators on a \u0000Hilbert space for a large class of interpolation methods. It is based on a simple new technique on \u0000“critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in \u0000particular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real <i>J</i>-method. Previously, \u0000such space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial \u0000derivations whose values on the critical points grow to infinity as slowly as we wish.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00028-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253201","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 the p-Dunford–Pettis relatively compact property of Banach spaces 论巴拿赫空间的 p-Dunford-Pettis 相对紧凑特性
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-29 DOI: 10.1007/s10476-024-00027-8
I. Ghenciu
{"title":"On the p-Dunford–Pettis relatively compact property of Banach spaces","authors":"I. Ghenciu","doi":"10.1007/s10476-024-00027-8","DOIUrl":"10.1007/s10476-024-00027-8","url":null,"abstract":"<div><p>The <i>p</i>-Dunford–Pettis relatively compact property (<span>(1le p&lt;infty)</span>)\u0000is studied in individual Banach spaces and in spaces of operators. The question\u0000of whether a space of operators has the <i>p</i>-Dunford–Pettis relatively compact\u0000property is studied using Dunford–Pettis <i>p</i>-convergent evaluation operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197201","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
Weighted weak-type iterated Hardy–Copson inequalities 加权弱型迭代哈代-科普森不等式
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-28 DOI: 10.1007/s10476-024-00021-0
V. García García, P. Ortega Salvador
{"title":"Weighted weak-type iterated Hardy–Copson inequalities","authors":"V. García García,&nbsp;P. Ortega Salvador","doi":"10.1007/s10476-024-00021-0","DOIUrl":"10.1007/s10476-024-00021-0","url":null,"abstract":"<div><p>We characterize the good weights for some weighted weak-type iterated Hardy-Copson inequalities to hold.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00021-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172524","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
Integral operators and Carleson measures for Möbius invariant Besov spaces 莫比乌斯不变贝索夫空间的积分算子和卡列松量
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-28 DOI: 10.1007/s10476-024-00029-6
W. Yang, C. Yuan
{"title":"Integral operators and Carleson measures for Möbius invariant Besov spaces","authors":"W. Yang,&nbsp;C. Yuan","doi":"10.1007/s10476-024-00029-6","DOIUrl":"10.1007/s10476-024-00029-6","url":null,"abstract":"<div><p>We investigate an integral operator <span>(T_{t,lambda})</span> which preserves\u0000the Carleson measure for the Möbius invariant Besov space <span>(B_p)</span> on the unit ball of <span>(mathbb{C}^{n})</span>. A holomorphic function space <span>(W_beta^p)</span>, associated with the Carleson measure for <span>(B_p)</span>, is introduced. As applications for the operator <span>(T_{t,lambda})</span>, we estimate the distance from Bloch-type functions to the space <span>(W_beta^p)</span>, which extends Jones' formula. Moreover, the bounded small Hankel operators on <span>(B_p)</span> and the atomic decomposition of <span>(W_beta^p)</span> are characterized.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172548","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 distribution of zeros of analytic functions in angles in (mathbf{C} backslash { {0}} ) 论 $$mathbf{C} 中角度解析函数零点的分布$$
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-28 DOI: 10.1007/s10476-024-00016-x
A. Fernández Árias
{"title":"On the distribution of zeros of analytic functions in angles in (mathbf{C} backslash { {0}} )","authors":"A. Fernández Árias","doi":"10.1007/s10476-024-00016-x","DOIUrl":"10.1007/s10476-024-00016-x","url":null,"abstract":"<div><p>In this article some results on the value distribution theory of analytic\u0000functions defined in angles of <span>(mathbb{C})</span>, due mainly to B. Ja. Levin and A. Pfluger,\u0000will be extended to the more general situation where the functions are defined in\u0000angles of <span>(mathbb{C}backslash{ 0})</span>. More precisely, angles <span>(S ( theta_{1},theta_{2}) )</span> with vertex at the origin will be\u0000considered and where a singularity at zero is allowed. An special class of these\u0000functions are those of completely regular growth for which it is proved a basic result\u0000which yields an expression of the density of its zeros in terms of the indicator\u0000function.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00016-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172522","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
Hyperinvariant subspaces for operators intertwined with weighted shift operators 与加权移位算子交织的算子的超不变子空间
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-23 DOI: 10.1007/s10476-024-00023-y
Z. Dali, A. Segres
{"title":"Hyperinvariant subspaces for operators intertwined with weighted shift operators","authors":"Z. Dali,&nbsp;A. Segres","doi":"10.1007/s10476-024-00023-y","DOIUrl":"10.1007/s10476-024-00023-y","url":null,"abstract":"<div><p>Suppose that <span>(T)</span> is an absolutely continuous polynomially bounded operator, <span>(S_{omega})</span> is a bilateral weighted shift, there exists a <span>(phiin mathbb{H}^{infty})</span> such that <span>(ker phi(S_{omega}^{*})neq {0})</span> and \u0000 a nonzero operator <span>(X)</span> such that <span>(S^{(infty)}_{omega}X=XT)</span>, where <span>(S^{(infty)}_{omega})</span> is the infinite countable orthogonal sum of copies of <span>(S_{omega})</span>. We prove that <span>(T)</span> has nontrivial hyperinvariant subspaces, that are the closures of <span>(text{Ran} psi(T))</span> for some <span>(psi in mathbb{H}^{infty})</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102428","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
Approximation in modified Zorko spaces 修正的佐科空间中的逼近
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-23 DOI: 10.1007/s10476-024-00025-w
D. Hasanah, H. Gunawan
{"title":"Approximation in modified Zorko spaces","authors":"D. Hasanah,&nbsp;H. Gunawan","doi":"10.1007/s10476-024-00025-w","DOIUrl":"10.1007/s10476-024-00025-w","url":null,"abstract":"<div><p>The set of smooth functions is not dense in Morrey spaces. To address the density issue in Morrey spaces, Zorko spaces are defined by utilizing the difference of a function of first order. In this paper, we propose a subspace of Morrey spaces which is defined using the difference of a function of second order. Approximation properties in the new subspace are investigated and the relation with Zorko spaces is studied via properties of smoothness spaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141107345","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 decomposition theorem for unitary group representations on Kaplansky–Hilbert modules and the Furstenberg–Zimmer structure theorem 卡普兰斯基-希尔伯特模块上单元群表示的分解定理和弗斯滕贝格-齐美尔结构定理
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-23 DOI: 10.1007/s10476-024-00020-1
N. Edeko, M. Haase, H. Kreidler
{"title":"A decomposition theorem for unitary group representations on Kaplansky–Hilbert modules and the Furstenberg–Zimmer structure theorem","authors":"N. Edeko,&nbsp;M. Haase,&nbsp;H. Kreidler","doi":"10.1007/s10476-024-00020-1","DOIUrl":"10.1007/s10476-024-00020-1","url":null,"abstract":"<div><p>In this paper, a decomposition theorem for (covariant) unitary\u0000group representations on Kaplansky–Hilbert modules over Stone algebras is established,\u0000which generalizes the well-known Hilbert space case (where it coincides\u0000with the decomposition of Jacobs, deLeeuw and Glicksberg).</p><p>The proof rests heavily on the operator theory on Kaplansky–Hilbert modules,\u0000in particular the spectral theorem for Hilbert–Schmidt homomorphisms on\u0000such modules.</p><p>As an application, a generalization of the celebrated Furstenberg–Zimmer\u0000structure theorem to the case of measure-preserving actions of arbitrary groups\u0000on arbitrary probability spaces is established.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141106738","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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