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Computational Methods and Function Theory最新文献

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Invariance of Iterated Global Differential Operator for Slice Monogenic Functions 片状单原函数的迭代全局微分算子的不变性
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-06-26 DOI: 10.1007/s40315-024-00551-6
Chao Ding, Zhenghua Xu
{"title":"Invariance of Iterated Global Differential Operator for Slice Monogenic Functions","authors":"Chao Ding, Zhenghua Xu","doi":"10.1007/s40315-024-00551-6","DOIUrl":"https://doi.org/10.1007/s40315-024-00551-6","url":null,"abstract":"<p>In this article, we present the symmetry group of a global slice Dirac operator and its iterated ones. Further, the explicit forms of intertwining operators of the iterated global slice Dirac operator are given. At the end, we introduce a variant of the global slice Dirac operator, which allows functions considered to be defined on the whole Euclidean space. The invariance property and the intertwining operators of this variant of the global slice Dirac operator are also presented.\u0000</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Sharing and Stirling Numbers 价值共享和斯特林数字
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-06-22 DOI: 10.1007/s40315-024-00552-5
Aimo Hinkkanen, Ilpo Laine
{"title":"Value Sharing and Stirling Numbers","authors":"Aimo Hinkkanen, Ilpo Laine","doi":"10.1007/s40315-024-00552-5","DOIUrl":"https://doi.org/10.1007/s40315-024-00552-5","url":null,"abstract":"<p>Let <i>f</i> be an entire function and <i>L</i>(<i>f</i>) a linear differential polynomial in <i>f</i> with constant coefficients. Suppose that <i>f</i>, <span>(f')</span>, and <i>L</i>(<i>f</i>) share a meromorphic function <span>(alpha (z))</span> that is a small function with respect to <i>f</i>. A characterization of the possibilities that may arise was recently obtained by Lahiri. However, one case leaves open many possibilities. We show that this case has more structure than might have been expected, and that a more detailed study of this case involves, among other things, Stirling numbers of the first and second kinds. We prove that the function <span>(alpha )</span> must satisfy a linear homogeneous differential equation with specific coefficients involving only three free parameters, and then <i>f</i> can be obtained from each solution. Examples suggest that only rarely do single-valued solutions <span>(alpha (z))</span> exist, and even then they are not always small functions for <i>f</i>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Some Results of Mues, Bergweiler and Eremenko Concerning Differential Polynomials 论 Mues、Bergweiler 和 Eremenko 有关微分多项式的一些结果
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-06-11 DOI: 10.1007/s40315-024-00544-5
Mingliang Fang, Zhiying He, Yuefei Wang
{"title":"On Some Results of Mues, Bergweiler and Eremenko Concerning Differential Polynomials","authors":"Mingliang Fang, Zhiying He, Yuefei Wang","doi":"10.1007/s40315-024-00544-5","DOIUrl":"https://doi.org/10.1007/s40315-024-00544-5","url":null,"abstract":"","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141355700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundary Traces of Holomorphic Functions on the Unit Ball in $$mathbb {C}^n$$ $$mathbb {C}^n$$ 单位球上全态函数的边界轨迹
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-06-07 DOI: 10.1007/s40315-024-00549-0
William E. Gryc
{"title":"Boundary Traces of Holomorphic Functions on the Unit Ball in $$mathbb {C}^n$$","authors":"William E. Gryc","doi":"10.1007/s40315-024-00549-0","DOIUrl":"https://doi.org/10.1007/s40315-024-00549-0","url":null,"abstract":"","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141372071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fast Computation of Analytic Capacity 快速计算分析能力
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-06-07 DOI: 10.1007/s40315-024-00547-2
Mohamed M. S. Nasser, Christopher C. Green, Matti Vuorinen
{"title":"Fast Computation of Analytic Capacity","authors":"Mohamed M. S. Nasser, Christopher C. Green, Matti Vuorinen","doi":"10.1007/s40315-024-00547-2","DOIUrl":"https://doi.org/10.1007/s40315-024-00547-2","url":null,"abstract":"<p>A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman–Stein integral equation to compute the Szegő kernel and then the value of the derivative of the Ahlfors map at the point at infinity. The proposed method can be used for domains with smooth and piecewise smooth boundaries. When combined with conformal mappings, the method can be used for compact slit sets. Several numerical examples are presented to demonstrate the efficiency of the proposed method. We recover some known exact results and corroborate the conjectural subadditivity property of analytic capacity.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Infinite $$varphi $$ -Order Solutions of Second Order Linear Differential Equations 论二阶线性微分方程的无限 $$varphi $$ 阶解
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-05-29 DOI: 10.1007/s40315-024-00548-1
Hui Yu, Xiaomin Li
{"title":"On the Infinite $$varphi $$ -Order Solutions of Second Order Linear Differential Equations","authors":"Hui Yu, Xiaomin Li","doi":"10.1007/s40315-024-00548-1","DOIUrl":"https://doi.org/10.1007/s40315-024-00548-1","url":null,"abstract":"<p>In this paper, we consider the second order linear differential equation </p><p> where <i>A</i>, <i>B</i> and <i>F</i> with <span>(Bnot equiv 0)</span> are entire functions. We find some appropriate conditions on <i>A</i>, <i>B</i> and <i>F</i> in terms of the <span>(varphi )</span>-order which guarantee that every non-constant entire solution <i>f</i> of (†) has infinite <span>(varphi )</span>-order, along with an additional relation between the hyper-<span>(varphi )</span>-order of <i>f</i> and the <span>(varphi )</span>-order of the dominating coefficient in (†).</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 New Metric Associated with the Domain Boundary 与域边界相关的新度量
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-05-23 DOI: 10.1007/s40315-024-00545-4
Xingchen Song, Gendi Wang
{"title":"A New Metric Associated with the Domain Boundary","authors":"Xingchen Song, Gendi Wang","doi":"10.1007/s40315-024-00545-4","DOIUrl":"https://doi.org/10.1007/s40315-024-00545-4","url":null,"abstract":"<p>In this paper, we introduce a new metric <span>(tilde{c})</span> which is associated with the domain boundary for a Ptolemy space (<i>X</i>, <i>d</i>). Moreover, we study inclusion relations of <span>(tilde{c})</span> metric balls and some related hyperbolic type metric balls in subdomains of <span>({mathbb {R}}^n.)</span> In addition, we study distortion properties of the <span>(tilde{c})</span> metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the <span>(tilde{c})</span> metric.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Korenblum’s Principle for Bergman Spaces with Radial Weights 有径向权重的伯格曼空间的科伦布伦原理
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-05-18 DOI: 10.1007/s40315-024-00543-6
Iason Efraimidis, Adrián Llinares, Dragan Vukotić
{"title":"Korenblum’s Principle for Bergman Spaces with Radial Weights","authors":"Iason Efraimidis, Adrián Llinares, Dragan Vukotić","doi":"10.1007/s40315-024-00543-6","DOIUrl":"https://doi.org/10.1007/s40315-024-00543-6","url":null,"abstract":"<p>We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces <span>(A^p_w)</span> with arbitrary (non-negative and integrable) radial weights <i>w</i> in the case <span>(1le p&lt;infty )</span>. We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption <span>(liminf _{rrightarrow 0^+} w(r)&gt;0)</span>, we show that the principle fails whenever <span>(0&lt;p&lt;1)</span>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Good Lambda Inequalities and Musielak–Orlicz Hardy Spaces 良好的 Lambda 不等式和 Musielak-Orlicz Hardy 空间
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-05-16 DOI: 10.1007/s40315-024-00541-8
Timothy Ferguson
{"title":"Good Lambda Inequalities and Musielak–Orlicz Hardy Spaces","authors":"Timothy Ferguson","doi":"10.1007/s40315-024-00541-8","DOIUrl":"https://doi.org/10.1007/s40315-024-00541-8","url":null,"abstract":"","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140968971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Cesàro-like Operator from Besov Spaces to Some Spaces of Analytic Functions 从贝索夫空间到某些解析函数空间的类塞萨洛算子
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-05-15 DOI: 10.1007/s40315-024-00542-7
Fangmei Sun, Fangqin Ye, Liuchang Zhou
{"title":"A Cesàro-like Operator from Besov Spaces to Some Spaces of Analytic Functions","authors":"Fangmei Sun, Fangqin Ye, Liuchang Zhou","doi":"10.1007/s40315-024-00542-7","DOIUrl":"https://doi.org/10.1007/s40315-024-00542-7","url":null,"abstract":"<p>In this paper, for <span>(p&gt;1)</span> and <span>(s&gt;1)</span>, we characterize completely the boundedness and compactness of a Cesàro-like operator from the Besov space <span>(B_p)</span> into a Banach space <i>X</i> between the mean Lipschitz space <span>(Lambda ^s_{1/s})</span> and the Bloch space. In particular, for <span>(p=s=2)</span>, we complete a previous result from the literature.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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