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

✍ Scribed by Lee A. Rubel

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 281 KB
• Volume: 84
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0009

✦ 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 .