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Alternation theory in approximation by polynomials having bounded coefficients

✍ Scribed by Shusheng Xu


Publisher
Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
1994
Tongue
English
Weight
570 KB
Volume
10
Category
Article
ISSN
0168-9673

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Approximation by polynomials with bounde
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Let ΞΈ be a real number satisfying 1 < ΞΈ < 2, and let A(ΞΈ) be the set of polynomials with coefficients in {0, 1}, evaluated at ΞΈ . Using a result of Bugeaud, we prove by elementary methods that ΞΈ is a Pisot number when the set (A(ΞΈ) -A(ΞΈ) -A(ΞΈ)) is discrete; the problem whether Pisot numbers are the