Uniform Approximation by Rational Functions Having Restricted Denominators.

1979 ◽  
Author(s):  
G. D. Taylor ◽  
E. H. Kaufman ◽  
Jr
Keyword(s):  
Uniform Approximation ◽  
Rational Functions ◽  
Approximation By Rational Functions

scholarly journals On Uniform Approximation by Rational Functions with an Application to Chordal Cluster Sets

1969 ◽  
Vol 34 ◽  
pp. 143-148 ◽  
Author(s):  
J.T. Gresser
Keyword(s):  
Meromorphic Function ◽  
Uniform Approximation ◽  
Boundary Behavior ◽  
Rational Functions ◽  
Approximation Techniques ◽  
Bounded Set ◽  
Perfect Set ◽  
Approximation By Rational Functions ◽  
Bounded Sets ◽  
Geometric Nature

For a closed and bounded set E in the complex plane, let A(E) denote the collection of all functions continuous on E and analytic on E°, its interior; let R(E) denote the collection of all functions which are uniform limits on E of rational functions with poles outside E. Then let A denote the collection of all closed, bounded sets for which A(E) = R(E). The purpose of this paper is to formulate a condition on a set, which is essentially of a geometric nature, in order that the set belong to A. Then using approximation techniques, we shall construct a meromorphic function having a certain boundary behavior on a perfect set; this answers a question raised in [1].

Approximation by Rational Functions

1977 ◽  
Vol s2-15 (2) ◽  
pp. 319-328 ◽  
Author(s):  
P. Erdős ◽  
D. J. Newman ◽  
A. R. Reddy
Keyword(s):  
Rational Functions ◽  
Approximation By Rational Functions
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