发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - Complex Variables最新文献

筛选
英文 中文
On the irregular Riemann-Hilbert correspondence 关于不规则黎曼-希尔伯特对应关系
arXiv - MATH - Complex Variables Pub Date : 2024-08-08 DOI: arxiv-2408.04260
Andrea D'Agnolo, Masaki Kashiwara
{"title":"On the irregular Riemann-Hilbert correspondence","authors":"Andrea D'Agnolo, Masaki Kashiwara","doi":"arxiv-2408.04260","DOIUrl":"https://doi.org/arxiv-2408.04260","url":null,"abstract":"The original Riemann-Hilbert problem asks to find a Fuchsian ordinary\u0000differential equation with prescribed singularities and monodromy in the\u0000complex line. In the early 1980's Kashiwara solved a generalized version of the\u0000problem, valid on complex manifolds of any dimension. He presented it as a\u0000correspondence between regular holonomic D-modules and perverse sheaves. The analogous problem where one drops the regularity condition remained open\u0000for about thirty years. We solved it in the paper that received a 2024\u0000Frontiers of Science Award. Our construction requires in particular an\u0000enhancement of the category of perverse sheaves. Here, using some examples in\u0000dimension one, we wish to convey the gist of the main ingredients used in our\u0000work. This is a written account of a talk given by the first named author at the\u0000International Congress of Basic Sciences on July 2024 in Beijing.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Landen-type method for computation of Weierstrass functions 计算魏尔斯特拉斯函数的兰登式方法
arXiv - MATH - Complex Variables Pub Date : 2024-08-08 DOI: arxiv-2408.05252
Matvey Smirnov, Kirill Malkov, Sergey Rogovoy
{"title":"A Landen-type method for computation of Weierstrass functions","authors":"Matvey Smirnov, Kirill Malkov, Sergey Rogovoy","doi":"arxiv-2408.05252","DOIUrl":"https://doi.org/arxiv-2408.05252","url":null,"abstract":"We establish a version of the Landen's transformation for Weierstrass\u0000functions and invariants that is applicable to general lattices in complex\u0000plane. Using it we present an effective method for computing Weierstrass\u0000functions, their periods, and elliptic integral in Weierstrass form given\u0000Weierstrass invariants $g_2$ and $g_3$ of an elliptic curve. Similarly to the\u0000classical Landen's method our algorithm has quadratic rate of convergence.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global regularity for the $barpartial$-Neumann problem on pseudoconvex manifolds 伪凸流形上 $barpartial$-Neumann 问题的全局正则性
arXiv - MATH - Complex Variables Pub Date : 2024-08-08 DOI: arxiv-2408.04512
Tran Vu Khanh, Andrew Raich
{"title":"Global regularity for the $barpartial$-Neumann problem on pseudoconvex manifolds","authors":"Tran Vu Khanh, Andrew Raich","doi":"arxiv-2408.04512","DOIUrl":"https://doi.org/arxiv-2408.04512","url":null,"abstract":"We establish general sufficient conditions for exact (and global) regularity\u0000in the $barpartial$-Neumann problem on $(p,q)$-forms, $0 leq p leq n$ and\u0000$1leq q leq n$, on a pseudoconvex domain $Omega$ with smooth boundary\u0000$bOmega$ in an $n$-dimensional complex manifold $M$. Our hypotheses include\u0000two assumptions: 1) $M$ admits a function that is strictly plurisubharmonic\u0000acting on $(p_0,q_0)$-forms in a neighborhood of $bOmega$ for some fixed $0\u0000leq p_0 leq n$, $1 leq q_0 leq n$, or $M$ is a K\"ahler metric whose\u0000holomorphic bisectional curvature acting $(p,q)$-forms is positive; and 2)\u0000there exists a family of vector fields $T_epsilon$ that are transverse to the\u0000boundary $bOmega$ and generate one forms, which when applied to $(p,q)$-forms,\u0000$0 leq p leq n$ and $q_0 leq q leq n$, satisfy a \"weak form\" of the\u0000compactness estimate. We also provide examples and applications of our main theorems.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variability regions for the $n$-th derivative of bounded analytic functions 有界解析函数 n 次导数的可变区域
arXiv - MATH - Complex Variables Pub Date : 2024-08-07 DOI: arxiv-2408.04030
Gangqiang Chen
{"title":"Variability regions for the $n$-th derivative of bounded analytic functions","authors":"Gangqiang Chen","doi":"arxiv-2408.04030","DOIUrl":"https://doi.org/arxiv-2408.04030","url":null,"abstract":"Let $mathcal{H}$ be the class of all analytic self-maps of the open unit\u0000disk $mathbb{D}$. Denote by $H^n f(z)$ the $n$-th order hyperbolic derivative\u0000of $fin mathcal H$ at $zin mathbb{D}$. For $z_0in mathbb{D}$ and $gamma\u0000= (gamma_0, gamma_1 , ldots , gamma_{n-1}) in {mathbb D}^{n}$, let\u0000${mathcal H} (gamma) = {f in {mathcal H} : f (z_0) = gamma_0,H^1f (z_0) =\u0000gamma_1,ldots ,H^{n-1}f (z_0) = gamma_{n-1} }$. In this paper, we determine\u0000the variability region $V(z_0, gamma ) = { f^{(n)}(z_0) : f in {mathcal H}\u0000(gamma) }$, which can be called ``the generalized Schwarz-Pick Lemma of\u0000$n$-th derivative\". We then apply the generalized Schwarz-Pick Lemma to\u0000establish a $n$-th order Dieudonn'e's Lemma, which provides an explicit\u0000description of the variability region ${h^{(n)}(z_0): hin mathcal{H},\u0000h(0)=0,h(z_0) =w_0, h'(z_0)=w_1,ldots, h^{(n-1)}(z_0)=w_{n-1}}$ for given\u0000$z_0$, $w_0$, $w_1,dots,w_{n-1}$. Moreover, we determine the form of all\u0000extremal functions.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Koebe uniformization of nondegenerate domains with bounded gap-ratio 具有有界间隙率的非enerate域的柯贝均匀化
arXiv - MATH - Complex Variables Pub Date : 2024-08-07 DOI: arxiv-2408.03484
Yi Zhong
{"title":"Koebe uniformization of nondegenerate domains with bounded gap-ratio","authors":"Yi Zhong","doi":"arxiv-2408.03484","DOIUrl":"https://doi.org/arxiv-2408.03484","url":null,"abstract":"Koebe uniformization is a fundemental problem in complex analysis. In this\u0000paper, we use transboundary extremal length to show that every nondegenerate\u0000and uncountably connected domain with bounded gap-ratio is conformally\u0000homeomorphic to a circle domain.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Best constants in reverse Riesz-type inequalities for analytoc and co-analytic projections 解析投影和共解析投影的反向里兹型不等式中的最佳常数
arXiv - MATH - Complex Variables Pub Date : 2024-08-05 DOI: arxiv-2408.02453
Petar Melentijević
{"title":"Best constants in reverse Riesz-type inequalities for analytoc and co-analytic projections","authors":"Petar Melentijević","doi":"arxiv-2408.02453","DOIUrl":"https://doi.org/arxiv-2408.02453","url":null,"abstract":"begin{abstract} Let $P_+$ be the Riesz's projection operator and let $P_-= I\u0000- P_+$. We consider the inequalities of the following form $$\u0000|f|_{L^p(mathbb{T})}leq B_{p,s}|( |P_ + f | ^s + |P_- f |^s) ^{frac\u00001s}|_{L^p (mathbb{T})} $$ and prove them with sharp constant $B_{p,s}$ for $s\u0000in [p',+infty)$ and $1<pleq 2$ and $pgeq 9,$ where\u0000$p':=min{p,frac{p}{p-1}}.$ end{abstract}","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entire functions with an arithmetic sequence of exponents 具有指数算术序列的完整函数
arXiv - MATH - Complex Variables Pub Date : 2024-08-04 DOI: arxiv-2408.02096
Dallas Ruth, Khang Tran
{"title":"Entire functions with an arithmetic sequence of exponents","authors":"Dallas Ruth, Khang Tran","doi":"arxiv-2408.02096","DOIUrl":"https://doi.org/arxiv-2408.02096","url":null,"abstract":"For a given entire function $f(z)=sum_{j=0}^{infty}a_{j}z^{j}$, we study\u0000the zero distribution of $f_{r}(z)=sum_{jequiv rpmod m}a_{j}z^{j}$ where\u0000$minmathbb{N}$ and $0le r<m$. We find conditions under which the zeros of\u0000$f_{r}(z)$ lie on $m$ radial rays defined by $Im z^{m}=0$ and $Re z^{m}le0$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 lower bounds of the $p$-modulus of families 关于家系的 $p$ 模的下界
arXiv - MATH - Complex Variables Pub Date : 2024-08-03 DOI: arxiv-2408.01771
Evgeny Sevost'yanov, Zarina Kovba, Georgy Nosal
{"title":"On the lower bounds of the $p$-modulus of families","authors":"Evgeny Sevost'yanov, Zarina Kovba, Georgy Nosal","doi":"arxiv-2408.01771","DOIUrl":"https://doi.org/arxiv-2408.01771","url":null,"abstract":"We study the problem of the lower bounds of the modulus of families of paths\u0000of order $p,$ $p>n-1,$ and their connection with the geometry of domains\u0000containing the specified families. Among other things, we have proved an\u0000analogue of N\"akki's theorem on the positivity of the $p$-module of families\u0000of paths joining a pair of continua in the given domain. The geometry of\u0000domains with a strongly accessible boundary in the sense of the $p$-modulus of\u0000families of paths was also studied. We show that domains with a $p$-strongly\u0000accessible boundary with respect to a $p$-modulus, $p>n-1,$ are are finitely\u0000connected at their boundary. The mentioned result generalizes N\"akki's result,\u0000which was proved for uniform domains in the case of a conformal modulus.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasiconformal reflection with respect to the boundary of an isosceles trapezoid 关于等腰梯形边界的准等边反射
arXiv - MATH - Complex Variables Pub Date : 2024-08-03 DOI: arxiv-2408.01821
A. Kushaeva, K. Kushaeva, S. Nasyrov
{"title":"Quasiconformal reflection with respect to the boundary of an isosceles trapezoid","authors":"A. Kushaeva, K. Kushaeva, S. Nasyrov","doi":"arxiv-2408.01821","DOIUrl":"https://doi.org/arxiv-2408.01821","url":null,"abstract":"We establish an upper estimate for the coefficient of quasiconformal\u0000reflection with respect to the boundary of an arbitrary isosceles trapezoid in\u0000terms of its geometric parameters; the estimate improve the result obtained in\u0000the recent paper by S.~Nasyrov, T.~Sugawa and M.~Vuorinen.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A unified theory of regular functions of a hypercomplex variable 超复变正则函数的统一理论
arXiv - MATH - Complex Variables Pub Date : 2024-08-02 DOI: arxiv-2408.01523
Riccardo Ghiloni, Caterina Stoppato
{"title":"A unified theory of regular functions of a hypercomplex variable","authors":"Riccardo Ghiloni, Caterina Stoppato","doi":"arxiv-2408.01523","DOIUrl":"https://doi.org/arxiv-2408.01523","url":null,"abstract":"This work proposes a unified theory of regularity in one hypercomplex\u0000variable: the theory of $T$-regular functions. In the special case of\u0000quaternion-valued functions of one quaternionic variable, this unified theory\u0000comprises Fueter-regular functions, slice-regular functions and a\u0000recently-discovered function class. In the special case of Clifford-valued\u0000functions of one paravector variable, it encompasses monogenic functions,\u0000slice-monogenic functions, generalized partial-slice monogenic functions, and a\u0000variety of function classes not yet considered in literature. For $T$-regular\u0000functions over an associative $*$-algebra, this work provides integral\u0000formulas, series expansions, an Identity Principle, a Maximum Modulus Principle\u0000and a Representation Formula. It also proves some foundational results about\u0000$T$-regular functions over an alternative but nonassociative $*$-algebra, such\u0000as the real algebra of octonions.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信