Approximation by polynomials with bounded coefficients
| dc.contributor.author | Zaimi, Toufik | |
| dc.date.accessioned | 2022-04-27T02:00:56Z | |
| dc.date.available | 2022-04-27T02:00:56Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | Let θ be a real number satisfying 1 <θ< 2, and let A(θ ) be the set of polynomials with coefficients in {0, 1}, evaluated at θ. Using a result of Bugeaud, we prove by elementary methods that θ is a Pisot number when the set (A(θ ) − A(θ ) − A(θ )) is discrete; the problem whether Pisot numbers are the only numbers θ such that 0 is not a limit point of (A(θ ) − A(θ )) is still unsolved. We also determine the three greatest limit points of the quantities inf{c, c > 0, c ∈ C(θ )}, where C(θ ) is the set of polynomials with coefficients in {−1, 1}, evaluated at θ, and we find in particular infinitely many Perron numbers θ such that the sets C(θ ) are discrete. | ar |
| dc.identifier.uri | http://hdl.handle.net/123456789/12922 | |
| dc.language.iso | en | ar |
| dc.publisher | ELSEVIER | |
| dc.subject | Polynomial approximation | ar |
| dc.subject | Beta-expansion | ar |
| dc.subject | Pisot numbers | ar |
| dc.title | Approximation by polynomials with bounded coefficients | ar |
| dc.type | Article | ar |
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