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Restrictions of linear relations on invariant subspaces and group inverse 不变子空间和群逆上线性关系的限制
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-25 DOI: 10.1007/s10476-025-00087-4
S. V. Djordjević, I. Roque
{"title":"Restrictions of linear relations on invariant subspaces and group inverse","authors":"S. V. Djordjević,&nbsp;I. Roque","doi":"10.1007/s10476-025-00087-4","DOIUrl":"10.1007/s10476-025-00087-4","url":null,"abstract":"<div><p>In this paper, we will consider two notions of an invariant subspace for a linear relation: the first one is through the graph of a linear relation, and the second one is by using the resolvent function of a linear relation. Through some examples and preliminary results, it is shown that the second notion is more suitable when the spectral properties of liner relations are involved. In the second part of the paper, such a notion of an invariant subspace is allowed to develop, in a constructive way, the concept of group inverse for linear relations.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"423 - 445"},"PeriodicalIF":0.5,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00087-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168791","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
Entire solutions of the eiconal type partial differential equations in (mathbb{C}^2) 中斜型偏微分方程的全解 (mathbb{C}^2)
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-25 DOI: 10.1007/s10476-025-00086-5
L. Yang, W. Chen, Q. Wang
{"title":"Entire solutions of the eiconal type partial differential equations in (mathbb{C}^2)","authors":"L. Yang,&nbsp;W. Chen,&nbsp;Q. Wang","doi":"10.1007/s10476-025-00086-5","DOIUrl":"10.1007/s10476-025-00086-5","url":null,"abstract":"<div><p>This paper characterizes the entire solutions of the following eiconal type partial differential equations\u0000</p><div><div><span>$$u^2+(a_{1}u_{z_{1}}+a_{2}u_{z_{2}})^2=p,,,, u_{z_{1}}^2+(a_{0}u+a_{2}u_{z_{2}})^2=p ,$$</span></div></div><p>\u0000 and\u0000</p><div><div><span>$$(u+a_{1}u_{z_{1}})^2+(a_{0}u+a_{2}u_{z_{2}})^2=p,$$</span></div></div><p> where <i>p</i> is a polynomial in <span>(mathbb{C}^2)</span>, and <span>(a_{0},a_{1},a_{2})</span> are constants in <span>(mathbb{C})</span>. Descriptions are given and complemented by various examples.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"727 - 748"},"PeriodicalIF":0.5,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169960","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 cut norm and Sampling Lemmas for unbounded kernels 无界核的切范数和抽样引理
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-19 DOI: 10.1007/s10476-025-00090-9
P. T. Fekete, D. Kunszenti-Kovács
{"title":"The cut norm and Sampling Lemmas for unbounded kernels","authors":"P. T. Fekete,&nbsp;D. Kunszenti-Kovács","doi":"10.1007/s10476-025-00090-9","DOIUrl":"10.1007/s10476-025-00090-9","url":null,"abstract":"<div><p>Generalizing the bounded kernel results of Borgs, Chayes, Lovász, Sós and Vesztergombi \u0000[2], we prove two Sampling Lemmas for unbounded kernels with respect to the cut norm. On the one hand, we show that given a (symmetric) kernel <span>(Uin L^p([0,1]^2))</span> for some <span>(3&lt;p&lt;infty)</span>, the cut norm of a random <span>(k)</span>-sample of <span>(U)</span> is with high probability within <span>(O(k^{-frac14+frac{1}{4p}}))</span> of the cut norm of <span>(U)</span>. The cut norm of the sample has a strong bias to being larger than the original, allowing us to actually obtain a stronger high probability bound of order <span>(O(k^{-frac 12+frac1p+varepsilon}))</span> for how much smaller it can be (for any <span>(p&gt;2)</span> here). These results are then partially extended to the case of vector valued kernels.</p><p>On the other hand, we show that with high probability, the <span>(k)</span>-samples are also close to <span>(U)</span> in the cut metric, albeit with a weaker bound of order <span>(O((ln k)^{-frac12+frac1{2p}}))</span> (for any appropriate <span>(p&gt;2)</span>). As a corollary, we obtain that whenever <span>(Uin L^p)</span> with <span>(p&gt;4)</span>, the <span>(k)</span>-samples converge almost surely to <span>(U)</span> in the cut metric as <span>(ktoinfty)</span>.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"477 - 514"},"PeriodicalIF":0.5,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00090-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166563","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
Abelian theorems for a variant of the index Whittaker transform over ( mathscr{E'}(mathbb{R}_+)) 指标惠特克变换的一个变量的阿贝尔定理 ( mathscr{E'}(mathbb{R}_+))
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-19 DOI: 10.1007/s10476-025-00093-6
J. Maan, B. J. González, E. R. Negrín
{"title":"Abelian theorems for a variant of the index Whittaker transform over ( mathscr{E'}(mathbb{R}_+))","authors":"J. Maan,&nbsp;B. J. González,&nbsp;E. R. Negrín","doi":"10.1007/s10476-025-00093-6","DOIUrl":"10.1007/s10476-025-00093-6","url":null,"abstract":"<div><p>Our goal is to establish Abelian theorems for a variant of the\u0000index Whittaker transform over distributions of compact support.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"577 - 585"},"PeriodicalIF":0.5,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167296","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
Sparse bounds for maximally truncated oscillatory singular integrals with non-convolutional Hölder class kernels 具有非卷积Hölder类核的最大截断振荡奇异积分的稀疏界
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-19 DOI: 10.1007/s10476-025-00095-4
W. Sun, S. Wang
{"title":"Sparse bounds for maximally truncated oscillatory singular integrals with non-convolutional Hölder class kernels","authors":"W. Sun,&nbsp;S. Wang","doi":"10.1007/s10476-025-00095-4","DOIUrl":"10.1007/s10476-025-00095-4","url":null,"abstract":"<div><p> We investigate the sparse bound for maximal oscillatory singular integrals given by\u0000</p><div><div><span>$$T_{P,K}^*f(x)=sup_{epsilon&gt;0} bigg| int_{|x-y|&gt;epsilon}e^{iP(x,y)}K(x,y)f(y) , dy bigg| ,$$</span></div></div><p>\u0000where <span>(P(x,y))</span> is a real-valued polynomial on <span>(mathbb{R}^ntimes mathbb{R}^n)</span> and <span>(K)</span> is a Calderón–Zygmund non-convolutional type kernel. We show that <span>(T_{P,K}^*)</span> satisfies an <span>((r,r))</span>-sparse bound for <span>(1&lt;r&lt;2)</span>, which implies the weighted <span>(L^p(1&lt;p&lt;infty))</span> estimate for the operator <span>(T_{P,K}^*)</span>.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"687 - 704"},"PeriodicalIF":0.5,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167255","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 collectively (L)-weakly compact sets of operators 在集合(L) -弱紧算子集上
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-12 DOI: 10.1007/s10476-025-00088-3
E. Emelyanov
{"title":"On collectively (L)-weakly compact sets of operators","authors":"E. Emelyanov","doi":"10.1007/s10476-025-00088-3","DOIUrl":"10.1007/s10476-025-00088-3","url":null,"abstract":"<div><p>A set of bounded linear operators from a Banach space to a Banach lattice is collectively <span>(L)</span>-weakly compact whenever union of images of the unit ball is <span>(L)</span>-weakly compact. In the present note the Meyer-Nieberg duality theorem is extended to collectively <span>(L)</span>-weakly compact sets of operators, the relationship between collectively <span>(L)</span>-weakly compact sets and collectively almost limited sets is investigated, and the domination problem for collectively compact and collectively <span>(L)</span>-weakly compact sets is studied.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"447 - 455"},"PeriodicalIF":0.5,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164970","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 coefficients of functions with respect to general othonormal systems from classes ( Lip (alpha)) 关于类中一般正交系统的函数的傅里叶系数 ( Lip (alpha))
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-12 DOI: 10.1007/s10476-025-00091-8
B. Golubov, S. Volosivets
{"title":"Fourier coefficients of functions with respect to general othonormal systems from classes ( Lip (alpha))","authors":"B. Golubov,&nbsp;S. Volosivets","doi":"10.1007/s10476-025-00091-8","DOIUrl":"10.1007/s10476-025-00091-8","url":null,"abstract":"<div><p>Let <span>({varphi_n}^infty_{n=1})</span> be a real-valued orthonormal system in <span>(L^2[0,1])</span>, <span>(0&lt;alphaleq 1)</span>, <span>(0&lt;varepsilon&lt;alpha)</span>, and let <span>({c_n(f)}^infty_{n=1})</span> be a sequence of Fourier coefficients of <span>(fin L^2[0,1])</span> with respect to <span>({varphi_n}^infty_{n=1})</span>. We prove a sufficient condition on <span>({varphi_n}^infty_{n=1})</span> such that the series <span>(sum^infty_{k=1}k^{2(alpha-varepsilon)}c^2_k(f))</span> converges for any <span>(fin Lip (alpha))</span>. We check that the trigonometric system and the Haar system satisfy this condition. On the other hand, the condition is not fulfilled in general.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"515 - 524"},"PeriodicalIF":0.5,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164976","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
Notes on meromorphic functions that share three small functions with their (k)th order derivatives 关于具有(k)阶导数的三个小函数的亚纯函数的注释
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-12 DOI: 10.1007/s10476-025-00092-7
X. -H. Huang
{"title":"Notes on meromorphic functions that share three small functions with their (k)th order derivatives","authors":"X. -H. Huang","doi":"10.1007/s10476-025-00092-7","DOIUrl":"10.1007/s10476-025-00092-7","url":null,"abstract":"<div><p>In this paper, we investigate a uniqueness question of transcendental\u0000meromorphic functions sharing three distinct polynomials with their\u0000kth order derivatives, and investigate a uniqueness question of transcendental\u0000meromorphic functions sharing three distinct small functions with their <span>(k)</span>th order\u0000derivatives, where two of the three distinct small functions are two distinct\u0000finite values. The main results obtained in this paper improve the corresponding\u0000results from Mues–Steinmetz [5], Gundersen [4] and Frank–Schwick [6].</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"547 - 558"},"PeriodicalIF":0.5,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164969","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
Analogues of Fourier quasicrystals for a strip 条带的傅立叶准晶体的类似物
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-12 DOI: 10.1007/s10476-025-00089-2
S. Yu. Favorov
{"title":"Analogues of Fourier quasicrystals for a strip","authors":"S. Yu. Favorov","doi":"10.1007/s10476-025-00089-2","DOIUrl":"10.1007/s10476-025-00089-2","url":null,"abstract":"<div><p>We study a certain family of discrete measures with unit masses\u0000on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We\u0000prove a one-to-one correspondence between supports of measures from this family\u0000and zero sets of exponential polynomials with imaginary frequencies. This result\u0000is the special case of a general result on measures whose supports correspond to\u0000zero sets of absolutely convergent Dirichlet series with bounded spectrum.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"457 - 475"},"PeriodicalIF":0.5,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164975","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
Tiling Morrey spaces – as a dyadic toy model 平铺Morrey空间-作为一个二元玩具模型
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-12 DOI: 10.1007/s10476-025-00094-5
Y. Sawano, H. Tanaka
{"title":"Tiling Morrey spaces – as a dyadic toy model","authors":"Y. Sawano,&nbsp;H. Tanaka","doi":"10.1007/s10476-025-00094-5","DOIUrl":"10.1007/s10476-025-00094-5","url":null,"abstract":"<div><p>The goal of this paper is to introduce tiling Morrey spaces and their weighted counterparts. A condition under which weights ensure the boundedness of important operators is established. Weights similar to the Muckenhoupt class <span>(A_p)</span> within Morrey spaces are dealt with. \u0000 Additionally, a full characterization of the weights for which two-weight norm inequalities for linear positive operators hold in these spaces is given. Then new class dealt with in this paper contains the one introduced recently by Lerner.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"667 - 685"},"PeriodicalIF":0.5,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164971","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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