Approximation by polynomials with coefficients \(\pm 1\). (Q1590263)
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scientific article; zbMATH DE number 1547360
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation by polynomials with coefficients \(\pm 1\). |
scientific article; zbMATH DE number 1547360 |
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Approximation by polynomials with coefficients \(\pm 1\). (English)
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1 January 2001
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In response to a question of R. Kenyon, we prove that the set of polynomials with coefficients \(\pm 1\), evaluated at a fixed real number \(\theta\), is dense in \(\mathbb R\) for a.e.\(\theta \in (\sqrt{2},2)\). For \(\theta \in (1,\sqrt{2})\), a more complete result can be obtained by elementary methods.
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polynomial approximation
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digit expansions
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Pisot numbers
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