The Density of Rational Functions in Markov Systems: A Counterexample to a Conjecture of
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چکیده
We construct a family of in nite Markov systems on [ 1; 1] with the property that the rational functions from these systems are not dense in C[ 1; 1]. This gives counterexamples to a long standing conjecture of D.J. Newman. Key Words: Markov Systems, Rational Approximation, Muntz Polynomials Classi cation Numbers: 41A20, 41A50 Peter B. Borwein1 Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax, Nova Scotia B3H 3J5 CANADA Boris Shekhtman Department of Mathematics University of South Florida Tampa, FL 33620, U.S.A. 1Research supported in part by NSERC of Canada.
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