Maximally convergent rational approximants of meromorphic functions

2015 ◽  
Vol 107 ◽  
pp. 63-78 ◽  
Author(s):  
Hans-Peter Blatt
Keyword(s):  
Meromorphic Functions ◽  
Rational Approximants

scholarly journals On convergence of(μ,ν)-sequences of unisolvent rational approximants to meromorphic functions inCn

1985 ◽  
Vol 8 (4) ◽  
pp. 641-652 ◽  
Author(s):  
C. H. Lutterodt
Keyword(s):  
Lebesgue Measure ◽  
Meromorphic Functions ◽  
Rational Approximants ◽  
Dimensional Lebesgue Measure

A generalization of the classical Montessus de Ballore theorem inℂnand some related theorems are discussed. Non-Montessus type of convergence inℝ2ndimensional Lebesgue measure is presented linking it to a result of Gonĉar.

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.

scholarly journals On rational approximation in a ball inℂN

2000 ◽  
Vol 24 (5) ◽  
pp. 335-344
Author(s):  
P. W. Darko ◽  
S. M. Einstein-Matthews ◽  
C. H. Lutterodt
Keyword(s):  
Rational Approximation ◽  
Special Class ◽  
Meromorphic Functions ◽  
Rational Approximations ◽  
Rational Approximants

We study rational approximations of elements of a special class of meromorphic functions which are characterized by their holomorphic behavior near the origin in balls inℂNby means of their rational approximants. We examine two modes of convergence for this class: almost uniform-type convergence analogous to Montessus-type convergence and weaker form of convergence using capacity based on the classical Tchebychev constant. These methods enable us to generalize and extend key results of Pommeranke and Gonchar.

Further investigations on Fujimoto type strong uniqueness polynomials

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5203-5216
Author(s):  
Abhijit Banerjee ◽  
Bikash Chakraborty ◽  
Sanjay Mallick
Keyword(s):  
Meromorphic Functions ◽  
Future Research ◽  
Strong Uniqueness ◽  
Open Questions

Taking the question posed by the first author in [1] into background, we further exhaust-ably investigate existing Fujimoto type Strong Uniqueness Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of SUPM named Restricted SUPM and exhibit some results which will give us a new direction to discuss the characteristics of a SUPM. Moreover, throughout the paper, we pose a number of open questions for future research.

On Fixed Points of Meromorphic Functions f(z) and f(z + c), Δcf(z)

2019 ◽  
Vol 39 (5) ◽  
pp. 1277-1289
Author(s):  
Shuangting Lan ◽  
Zongxuan Chen
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions
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