Bernstein-walsh inequalities in higherdimensions over exponential curves
| dc.contributor.author | Kadyrov, Shirali | |
| dc.contributor.author | Lawrence, Mark | |
| dc.date.accessioned | 2015-12-28T06:13:51Z | |
| dc.date.available | 2015-12-28T06:13:51Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | Let x = (x1; : : : ; xd) 2 [1; 1]d be linearly independent over Z, set K = f(ez; ex1z; ex2z : : : ; exdz) : jzj 1g:We prove sharp estimates for the growth of a polynomial of degree n, in terms of En(x) := supfkPk d+1 : P 2 Pn(d + 1); kPkK 1g; where d+1 is the unit polydisk. For all x 2 [1; 1]d with linearly independent entries, we have the lower estimate logEn(x) nd+1 (d 1)!(d + 1) log n O(nd+1); for Diophantine x, we have logEn(x) nd+1 (d 1)!(d + 1) log n + O(nd+1): In particular, this estimate holds for almost all x with respect to Lebesgue measure. The results here generalize those of [6] for d = 1, without relying on estimates for best approximants of rational numbers which do not hold in the vector-valued setting. | ru_RU |
| dc.identifier.citation | Kadyrov Shirali, Lawrence Mark; 2011; Bernstein-walsh inequalities in higherdimensions over exponential curves | ru_RU |
| dc.identifier.uri | http://nur.nu.edu.kz/handle/123456789/978 | |
| dc.language.iso | en | ru_RU |
| dc.subject | Research Subject Categories::MATHEMATICS | ru_RU |
| dc.subject | bernstein-walsh inequalities | ru_RU |
| dc.title | Bernstein-walsh inequalities in higherdimensions over exponential curves | ru_RU |
| dc.type | Article | ru_RU |