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.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.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.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 |