Bernstein-Walsh inequalities and the exponential curve in ℂ2

Dan Coman; Evgeny A. Poletsky

doi:10.1090/S0002-9939-02-06571-1

Bernstein-Walsh inequalities and the exponential curve in ℂ²

Dan Coman, Evgeny A. Poletsky

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

It is shown that for the pluripolar set K = {(z, e^z): |z| ≤ 1} in ℂ² there is a global Bernstein-Walsh inequality: If P is a polynomial of degree n on ℂ² and |P| ≤ 1 on K, this inequality gives an upper bound for |P(z, w)| which grows like exp(1/2n² log n). The result is used to obtain sharp estimates for |P(z, e^z)|.

Original language	English (US)
Pages (from-to)	879-887
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-02-06571-1
State	Published - Mar 2003

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-02-06571-1

Fingerprint Dive into the research topics of 'Bernstein-Walsh inequalities and the exponential curve in ℂ<sup>2</sup>'. Together they form a unique fingerprint.

Cite this

@article{3d950b89c9684af8bbaf050dd92e633e,

title = "Bernstein-Walsh inequalities and the exponential curve in ℂ2",

abstract = "It is shown that for the pluripolar set K = {(z, ez): |z| ≤ 1} in ℂ2 there is a global Bernstein-Walsh inequality: If P is a polynomial of degree n on ℂ2 and |P| ≤ 1 on K, this inequality gives an upper bound for |P(z, w)| which grows like exp(1/2n2 log n). The result is used to obtain sharp estimates for |P(z, ez)|.",

author = "Dan Coman and Poletsky, {Evgeny A.}",

year = "2003",

month = mar,

doi = "10.1090/S0002-9939-02-06571-1",

language = "English (US)",

volume = "131",

pages = "879--887",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Bernstein-Walsh inequalities and the exponential curve in ℂ2

AU - Coman, Dan

AU - Poletsky, Evgeny A.

PY - 2003/3

Y1 - 2003/3

N2 - It is shown that for the pluripolar set K = {(z, ez): |z| ≤ 1} in ℂ2 there is a global Bernstein-Walsh inequality: If P is a polynomial of degree n on ℂ2 and |P| ≤ 1 on K, this inequality gives an upper bound for |P(z, w)| which grows like exp(1/2n2 log n). The result is used to obtain sharp estimates for |P(z, ez)|.

AB - It is shown that for the pluripolar set K = {(z, ez): |z| ≤ 1} in ℂ2 there is a global Bernstein-Walsh inequality: If P is a polynomial of degree n on ℂ2 and |P| ≤ 1 on K, this inequality gives an upper bound for |P(z, w)| which grows like exp(1/2n2 log n). The result is used to obtain sharp estimates for |P(z, ez)|.

UR - http://www.scopus.com/inward/record.url?scp=0037374571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037374571&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-02-06571-1

DO - 10.1090/S0002-9939-02-06571-1

M3 - Article

AN - SCOPUS:0037374571

VL - 131

SP - 879

EP - 887

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3