Holomorphic and harmonic approximation on Riemann surfaces

被引:0
作者
Boivin, A [1 ]
Gauthier, PM [1 ]
机构
[1] Univ Western Ontario, Dept Math, London, ON N4G 5B7, Canada
来源
APPROXIMATION, COMPLEX ANALYSIS, AND POTENTIAL THEORY | 2001年 / 37卷
关键词
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The most important result on open Riemann surfaces is the analog of Runge's theorem on approximation by complex polynomials, due to Behnke and Stein. In this course, we begin by a discussion of Runge's theorems on polynomial and rational approximation on compact sets. This theory is refined and extended in various ways to Riemann surfaces. We also introduce a corresponding theory of harmonic approximation.
引用
收藏
页码:107 / 128
页数:22
相关论文
共 50 条
[32]   HOLOMORPHIC FAMILIES OF COMPACT RIEMANN SURFACES WITH AUTOMORPHISMS [J].
GUERRERO, I .
ILLINOIS JOURNAL OF MATHEMATICS, 1982, 26 (02) :212-225
[33]   RIEMANN SURFACES AND BOUNDED HOLOMORPHIC-FUNCTIONS [J].
PRANGER, W .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 259 (02) :393-400
[34]   Measured solenoidal Riemann surfaces and holomorphic dynamics [J].
Su, MY .
JOURNAL OF DIFFERENTIAL GEOMETRY, 1997, 47 (01) :170-195
[35]   HOLOMORPHIC MAPPINGS BETWEEN COMPACT RIEMANN SURFACES [J].
Ito, Manabu ;
Yamamoto, Hiroshi .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2009, 52 :109-126
[36]   FREQUENCY OF CONTINUABLE HOLOMORPHIC FUNCTIONS ON RIEMANN SURFACES [J].
KODITZ, H .
MATHEMATISCHE ZEITSCHRIFT, 1975, 143 (02) :145-148
[37]   CARLEMAN APPROXIMATION ON RIEMANN SURFACES [J].
BOIVIN, A .
MATHEMATISCHE ANNALEN, 1986, 275 (01) :57-70
[38]   VEECH HOLOMORPHIC FAMILIES OF RIEMANN SURFACES, HOLOMORPHIC SECTIONS, AND DIOPHANTINE PROBLEMS [J].
Shinomiya, Yoshihiko .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (06) :3161-3190
[39]   Harmonic and holomorphic prym differentials on a compact riemann surface [J].
Chueshev V.V. .
Siberian Mathematical Journal, 1999, 40 (2) :402-411
[40]   Harmonic and holomorphic Prym differentials on a compact Riemann surface [J].
Chueshev, VV .
SIBERIAN MATHEMATICAL JOURNAL, 1999, 40 (02) :402-411