On the Convergence in Capacity of Rational Approximants

2001 ◽  
Vol 17 (1) ◽  
pp. 91-102 ◽  
Author(s):  
T. Bloom
Keyword(s):  
Rational Approximants ◽  
Convergence In Capacity

scholarly journals Convergence in capacity of rational approximants of meromorphic functions

2014 ◽  
Vol 96 (110) ◽  
pp. 31-39 ◽  
Author(s):  
Hans-Peter Blatt
Keyword(s):  
Convergence Rate ◽  
Meromorphic Functions ◽  
Compact Set ◽  
Rational Approximants ◽  
Geometric Convergence ◽  
Convergence In Capacity

Let f be meromorphic on the compact set E ? C with maximal Green domain of meromorphy Ep(f), p(f) < ?. We investigate rational approximants with numerator degree ? n and denominator degree ? mn for f. We show that the geometric convergence rate on E implies convergence in capacity outside E if mn = o(n) as n ? 1. Further, we show that the condition is sharp and that the convergence in capacity is uniform for a subsequence ? ? N.

Rational approximants generated by the u-transform

1993 ◽  
Vol 78 (1-2) ◽  
pp. 29-54 ◽  
Author(s):  
Dhiranjan Roy ◽  
Ranjan Bhattacharya ◽  
Siddhartha Bhowmick
Keyword(s):  
Rational Approximants

scholarly journals Convergence in capacity and applications

2010 ◽  
Vol 107 (1) ◽  
pp. 90 ◽  
Author(s):  
Pham Hoang Hiep
Keyword(s):  
Weak Topology ◽  
Convergence In Capacity

In this article we prove that if $u_j, v_j, w\in\mathcal{E}(\Omega)$ such that $u_j,v_j\geq w$, $\forall\ j\geq 1$, and $|u_j-v_j|\to 0$ in $C_n$-capacity, then $\lim_{j\to\infty}h(\varphi_1,\ldots,\varphi_m) [(dd^cu_j)^n-(dd^cv_j)^n]=0$ in the weak-topology of measures for all $\varphi_1,\ldots ,\varphi_m\in{\operatorname{PSH}}\cap L_{\operatorname {loc}}^\infty (\Omega)$, $h\in C(\mathsf{R}^m)$. We shall then use this result to give some applications.

Convergence in capacity on smooth hypersurfaces of compact Kähler manifolds

2012 ◽  
Vol 103 (2) ◽  
pp. 175-187
Author(s):  
Vu Viet Hung ◽  
Hoang Nhat Quy
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Convergence In Capacity
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