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The value distribution of random analytic functions on the unit disk
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-10-17 DOI: 10.1007/s10476-024-00041-w
H. LI, Z. Ye
{"title":"The value distribution of random analytic functions on the unit disk","authors":"H. LI,&nbsp;Z. Ye","doi":"10.1007/s10476-024-00041-w","DOIUrl":"10.1007/s10476-024-00041-w","url":null,"abstract":"<div><p>We study the value distributions of the random analytic functions on the unit disk of the form \u0000</p><div><div><span>$$f_omega(z)= sum _{j=0}^{infty}chi_j(omega) a_j z^j,$$</span></div></div><p>\u0000where <span>(a_jinmathbb{C})</span> and <span>(chi_j(omega))</span> are independent and identically distributed random variables defined on a probability space <span>((Omega, mathcal{F}, mu))</span>. Some of the theorems complement the work in\u0000 [6], \u0000which deals with random entire functions.\u0000We first define a family of random analytic functions in the above form, which includes Gaussian, Rademacher, and Steinhaus analytic functions. Then we prove the relationship between the integrated counting function <span>(N(r, a, f_omega))</span>\u0000and the <span>(L_2)</span> norm of <span>(f)</span> on the circle <span>(|z|=r)</span> as <span>(r)</span> is close to <span>(1)</span>. As a by-product, we obtain Nevanlinna's second main theorem on the unit disk. Finally, we show theorems on the maximum modulus of <span>(f)</span> and <span>(f_omega)</span> on the unit disk.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"255 - 268"},"PeriodicalIF":0.6,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706918","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 note on the Huijsmans–de Pagter problem on finite dimensional ordered vector spaces 有限维有序向量空间上的Huijsmans-de Pagter问题
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-10-02 DOI: 10.1007/s10476-024-00052-7
C. Badea, J. Glück
{"title":"A note on the Huijsmans–de Pagter problem on finite dimensional ordered vector spaces","authors":"C. Badea,&nbsp;J. Glück","doi":"10.1007/s10476-024-00052-7","DOIUrl":"10.1007/s10476-024-00052-7","url":null,"abstract":"<div><p>A classical problem posed in 1992 by Huijsmans and de Pagter asks whether, for every positive operator <span>(T)</span> on a Banach lattice with spectrum <span>(sigma(T) = {1})</span>, the inequality <span>(T ge operatorname{id})</span> holds true. While the problem remains unsolved in its entirety, a positive solution is known in finite dimensions. In the broader context of ordered Banach spaces, Drnovšek provided an infinite-dimensional counterexample. In this note, we demonstrate the existence of finite-dimensional counterexamples, specifically on the ice cream cone and on a polyhedral cone in <span>(mathbb{R}^3)</span>. On the other hand, taking inspiration from the notion of <span>(m)</span>-isometries, we establish that each counterexample must contain a Jordan block of size at least <span>(3)</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 4","pages":"1009 - 1017"},"PeriodicalIF":0.6,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859477","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 necessary condition for the boundedness of the maximal operator on (L^{p(cdot)}) over reverse doubling spaces of homogeneous type
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-10-02 DOI: 10.1007/s10476-024-00053-6
O. Karlovych, A. Shalukhina
{"title":"A necessary condition for the boundedness of the maximal operator on (L^{p(cdot)}) over reverse doubling spaces of homogeneous type","authors":"O. Karlovych,&nbsp;A. Shalukhina","doi":"10.1007/s10476-024-00053-6","DOIUrl":"10.1007/s10476-024-00053-6","url":null,"abstract":"<div><p>Let <span>((X,d,mu))</span> be a space of homogeneous type and <span>(p(cdot) colon X to[1,infty])</span> be a variable exponent. We show that if the measure <span>(mu)</span> is Borel-semiregular and reverse doubling, then the condition \u0000<span>({ess,inf}_{xin X}p(x)&gt;1)</span> \u0000is necessary for the boundedness of the Hardy–Littlewood maximal operator <span>(M)</span> \u0000on the variable Lebesgue space <span>(L^{p(cdot)}(X,d,mu))</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"241 - 248"},"PeriodicalIF":0.6,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00053-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706885","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
Curves in the Fourier zeros of polytopal regions and the Pompeiu problem 多边形区域的傅立叶零点曲线与庞培问题
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-27 DOI: 10.1007/s10476-024-00054-5
M. N. Kolountzakis, E. Spyridakis
{"title":"Curves in the Fourier zeros of polytopal regions and the Pompeiu problem","authors":"M. N. Kolountzakis,&nbsp;E. Spyridakis","doi":"10.1007/s10476-024-00054-5","DOIUrl":"10.1007/s10476-024-00054-5","url":null,"abstract":"<div><p>We prove that any finite union <i>P</i> of interior-disjoint polytopes in <span>(mathbb R^d)</span> has the Pompeiu property, a result first proved by Williams \u0000[15]. This means that if a continuous function <i>f</i> on <span>(mathbb R^d)</span> integrates to 0 on any congruent copy of <span>(P)</span> then <span>(f)</span> is identically 0. By a fundamental result of Brown, Schreiber and Taylor \u0000[4], this is equivalent to showing that the Fourier–Laplace transform of the indicator function of <i>P</i> does not vanish identically on any 0-centered complex sphere in <span>(mathbb C^d)</span>. Our proof initially follows the recent one of Machado and Robins \u0000[12] who are using the Brion–Barvinok formula for the Fourier–Laplace transform of a polytope. But we simplify this method considerably by removing the use of properties of Bessel function zeros. Instead we use some elementary arguments on the growth of linear combinations of exponentials with rational functions as coefficients. Our approach allows us to prove the non-existence of complex spheres of any center in the zero-set of the Fourier–Laplace transform. The planar case is even simpler in that we do not even need the Brion–Barvinok formula. We then go further in the question of which sets can be contained in the null set of the Fourier–Laplace transform of a polytope by extending results of Engel \u0000[7] who showed that rationally parametrized hypersurfaces, under some mild conditions, cannot be contained in this null-set. We show that a rationally parametrized <i>curve</i> which is not contained in an affine hyperplane in <span>(mathbb C^d)</span> cannot be contained in this null-set. Results about curves parametrized by meromorphic functions are also given.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 4","pages":"1081 - 1098"},"PeriodicalIF":0.6,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859503","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 by a special de la Vallée Poussin type matrix transform mean of Vilenkin–Fourier series 维伦金-傅里叶级数的特殊德瓦雷-普桑型矩阵变换均值近似法
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-16 DOI: 10.1007/s10476-024-00049-2
I. Blahota, D. Nagy
{"title":"Approximation by a special de la Vallée Poussin type matrix transform mean of Vilenkin–Fourier series","authors":"I. Blahota,&nbsp;D. Nagy","doi":"10.1007/s10476-024-00049-2","DOIUrl":"10.1007/s10476-024-00049-2","url":null,"abstract":"<div><p>We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system. \u0000We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of \u0000continuity of the function. We also give theorems with respect to norm and almost everywhere convergences.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"939 - 957"},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264977","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
Value cross-sharing problems on meromorphic functions 分形函数的值交叉共享问题
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-16 DOI: 10.1007/s10476-024-00051-8
Y. C. Gao, K. Liu, F. N. Wang
{"title":"Value cross-sharing problems on meromorphic functions","authors":"Y. C. Gao,&nbsp;K. Liu,&nbsp;F. N. Wang","doi":"10.1007/s10476-024-00051-8","DOIUrl":"10.1007/s10476-024-00051-8","url":null,"abstract":"<div><p>In this paper, we continue to consider the value cross-sharing problems on meromorphic functions. We mainly present some results and improvements on <span>(f(z))</span> and <span>(g(z))</span> provided that <span>(f(z))</span> and <span>(g^{(k)}(z))</span> share common values together with <span>(g(z))</span> and <span>(f^{(k)}(z))</span> share the same or different common values CM or IM, where <span>(f(z), g(z))</span> are meromorphic functions and <span>(k)</span> is a positive integer. With additional conditions on deficiency, we get more accurate relations on <span>(f(z))</span> and <span>(g(z))</span> when <span>(f(z))</span> and <span>(g^{(k)}(z))</span> share a CM together with <span>(g(z))</span> and <span>(f^{(k)}(z))</span> share <i>b</i> CM, where <i>a</i>, <i>b</i> are constants.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"191 - 209"},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00051-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264975","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
Large dilates of hypercube graphs in the plane 平面超立方体图的大扩张
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-15 DOI: 10.1007/s10476-024-00045-6
V. Kovač, B. Predojević
{"title":"Large dilates of hypercube graphs in the plane","authors":"V. Kovač,&nbsp;B. Predojević","doi":"10.1007/s10476-024-00045-6","DOIUrl":"10.1007/s10476-024-00045-6","url":null,"abstract":"<div><p>We study a distance graph <span>(Gamma_n)</span> that is isomorphic to the <span>(1)</span>-skeleton of an <span>(n)</span>-dimensional unit hypercube. We show that every measurable set of positive upper Banach density in the plane contains all sufficiently large dilates of <span>(Gamma_n)</span>. This provides the first examples of distance graphs other than the trees for which a dimensionally sharp embedding in positive density sets is known.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"893 - 915"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264970","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
Decomposable operators acting between distinct (L^p)-direct integrals of Banach spaces 作用于巴拿赫空间不同 $$L^p$$ 直接积分之间的可分解算子
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-15 DOI: 10.1007/s10476-024-00044-7
N. Evseev, A. Menovschikov
{"title":"Decomposable operators acting between distinct (L^p)-direct integrals of Banach spaces","authors":"N. Evseev,&nbsp;A. Menovschikov","doi":"10.1007/s10476-024-00044-7","DOIUrl":"10.1007/s10476-024-00044-7","url":null,"abstract":"<div><p>The notion of decomposable operators acting between distinct <span>(L^p)</span>-direct \u0000integrals of Banach spaces is introduced. We show that these operators generalize the composition operator in the sense that a binary relation replaces a \u0000mapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"861 - 892"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264971","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 inequalities of Zygmund and de Bruijn 关于齐格蒙德和德布鲁因的不等式
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-15 DOI: 10.1007/s10476-024-00048-3
R. R. Akopyan, P. Kumar, G. V. Milovanović
{"title":"On the inequalities of Zygmund and de Bruijn","authors":"R. R. Akopyan,&nbsp;P. Kumar,&nbsp;G. V. Milovanović","doi":"10.1007/s10476-024-00048-3","DOIUrl":"10.1007/s10476-024-00048-3","url":null,"abstract":"<div><p>For the polar derivative <span>(D_alpha P(z) =nP(z)+(alpha-z)P'(z))</span> of \u0000a polynomial <span>(P(z))</span> of degree <i>n</i>, most of \u0000the <span>(L^p)</span> inequalities available in the literature are for restricted values of <span>(alpha)</span>, and in this \u0000paper we extend few such fundamental results to all of <span>(alpha)</span> in the complex plane.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 4","pages":"967 - 986"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264973","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
An asymptotic equality of Cartan's Second Main Theorem and some generalizations 卡坦第二主定理的渐进相等性和一些概论
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-09-15 DOI: 10.1007/s10476-024-00043-8
Y. Chen
{"title":"An asymptotic equality of Cartan's Second Main Theorem and some generalizations","authors":"Y. Chen","doi":"10.1007/s10476-024-00043-8","DOIUrl":"10.1007/s10476-024-00043-8","url":null,"abstract":"<div><p>Motivated by [19] and [10], we define the modified proximity function <span>(overline{m}_{q}(f,r))</span> \u0000for entire curves in complex projective space <span>(mathbf{P}^nmathbf{C})</span>, and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of \u0000[19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"129 - 163"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264976","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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