arXiv math/03112292003-11-13math.CV

T-universal Functions With Prescribed Approximation Curves

Daniel Mayenberger

备注：: References corrected

英文摘要：

Let be F a family of curves in the unit disc. We show that the set of all functions f holomorphic on the unit disc, which satisfy the following condition, is G-delta and dense in the space of all functions holomorphic on the unit disc: For each compact set K with connected complement, each function g continuous on K and holomorphic on its interior, every point t on the unit circle, every curve C in F (ending in t) and any e>0 there exist numbers 0<a<1 and b in C such that |f(az+b)-g(z)|<e for all z in K and |b-t|<e. The set of these functions is called the class of T-universal functions with prescribed approximation curves.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

具有指定叶状结构数的曲线的邻域

Neighborhoods of curves with a prescribed number of foliations

Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Pontificia Universidad Católica del Perú（秘鲁天主教 Pontificia 大学）

本研究针对n维射影空间中连通射影曲线的邻域问题，构造了恰好带指定数目余维1全纯叶状结构的n维非紧复流形，确定其亚纯函数域的可能形式，推广并改进了曲面情形的相关结果。

2026-08-04math.AGmath.CV

Universal Taylor series with respect to a prescribed subsequence

For a holomorphic function $f$ in the open unit disc $\mathbb{D}$ and $ζ\in\mathbb{D}$, $S_n(f,ζ)$ denotes the $n$-th partial sum of the Taylor development of $f$ at $ζ$. Given an increasing sequence of positive integers $μ=(μ_n)$, we consider the classes $\mathcal{U}(\mathbb{D},ζ)$ (resp. $\mathcal{U}^{(μ)}(\mathbb{D},ζ)$) of such functions $f$ such that the partial sums $\{S_n(f,ζ):n=1,2,\dots\}$ (resp. $\{S_{μ_n}(f,ζ):n=1,2,\dots\}$) approximate all polynomials uniformly on the compact sets $K\subset\{z\in\mathbb{C}:\vert z\vert\geq 1\}$ with connected complement. We show that these two cla…

2020-10-23math.CAmath.CVmath.FA

全纯勒让德曲线的逼近及其射流插值

Approximation of holomorphic Legendrian curves with jet-interpolation

该文证明全纯勒让德曲线的插值与逼近定理，包括可数点集位于浸入曲面及Carleman型逼近，并给出适当嵌入条件。

2023-05-16math.CV

Subclasses of Universal Taylor Series and center independence

A holomorphic function f on a simply connected domain $Ω$ belongs to a subclass of universal Taylor series if prescribed and infinite number of partial sums of the Taylor expansion of f around a given center $ζ_0$ realize Mergalyan-type approximations outside $Ω$. We will prove that this class is independent of the choice of center if the indices of the partial sums do not grow very fast to infinity.

2020-02-09math.CV

有限 Blaschke 乘积与有界泛函函数的同时逼近

Simultaneous Approximation by Finite Blaschke Products and Bounded Universal Functions

本文研究有限 Blaschke 乘积的同时逼近问题，证明其可同时逼近单位圆盘内的有界全纯函数和圆周零测度紧子集上的单位模连续函数，并应用于构造具有泛函边界行为的有界全纯函数。

2025-11-09math.CV

Envelopes of positive metrics with prescribed singularities

We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C^{1,1} regularity of such envelopes, showing their Monge-Ampere measure is supported on a certain "equilibrium set" and connecting with the asymptotics of the partial Bergman functions coming from multiplier ideals. We investigate how these envelopes behave on certain products, and how they relate to the Legendre transform of a test curve of singularity types in the context of geodesic rays in the space of Kähler potentials. Finally we consider the assoc…

2016-07-15math.CV

更多相关论文收起更多论文

射影空间中增长缓慢的通用整曲线

Universal Entire Curves in Projective Spaces with Slow Growth

本文构造射影空间中的显式通用整曲线，使其 Nevanlinna 特征函数增长慢于任意预定超越增长率，并在给定可数方向的平移下超循环。

2023-07-15math.CV

Velling-Kirillov metric on the universal Teichmuller curve

We extend Velling's approach and prove that the second variation of the spherical areas of a family of domains defines a Hermitian metric on the universal Teichmuller curve, whose pull back to Diff+(S^1)/S^1 coincides with the Kirillov metric. We show that the vertical integration of the square of the symplectic form of Velling-Kirillov metric on the universal Teichmuller curve is the symplectic form that defines the Weil-Petersson metric on the universal Teichmuller space. Restricted to a finite dimensional Teichmuller space, the vertical integration of the corresponding form on the Teichmull…

2002-10-14math.CV

Complex curves in pseudoconvex Runge domains containing discrete subsets

For any pseudoconvex Runge domain $Ω\subset\mathbb{C}^2$ we prove that every closed discrete subset in $Ω$ is contained in a properly embedded complex curve in $Ω$ with any prescribed topology (possibly infinite).

2018-01-04math.CVmath.DG

Embedded Curves and Foliations

We prove the existence of regular foliations with a prescribed tangency divisor in neighborhoods of negatively embedded holomorphic curves; this is related to a linearization theorem due to Grauert. We give also examples of neighborhoods which can not be linearized.

2011-10-17math.AGmath.CV

Universal locally univalent functions and universal conformal metrics with constant curvature

We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk. These results are used to prove that on any hyperbolic simply connected plane domain there exist universal conformal metrics with prescribed constant curvature.

2018-04-03math.APmath.CVmath.DG

Nondegenerate germs of holomorphic foliations with prescribed holonomy

We are interested in characterizing the holonomy maps associated to integral curves of non-degenerate singularities of holomorphic vector fields. Such a description is well-known in dimension 2 where is a key ingredient in the study of reduced singularities. The most intricate case in the 2 dimensional setting corresponds to (Siegel) saddle singularities. This work treats the analogous problem for saddles in higher dimension. We show that any germ of holomorphic biholomorphism, in any dimension, can be obtained as the holonomy map associated to an integral curve of a saddle singularity. A natu…

2023-01-23math.CAmath.CVmath.DS