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Uniform Approximation by Rational Functions Which All Satisfy the Same Algebraic Differential Equation

โœ Scribed by Lee A. Rubel


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
281 KB
Volume
84
Category
Article
ISSN
0021-9045

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โœฆ Synopsis


dedicated to the fond memory of burrill b. crohn

We prove that given two disjoint compact sets K 1 and K 2 in the complex plane, without any holes in them, there exists a sequence p n (z) of rational functions, all of them satisfying one and the same algebraic differential equation, such that p n (z) converges uniformly to 1 on K 1 and uniformly to 0 on K 2 .


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