Bernstein classes

N. Roytwarf; Yosef Yomdin

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 3, page 825-858
  • ISSN: 0373-0956

Abstract

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One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes R . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions. We present in detail various properties of the classes of functions, satisfying Bernstein type inequalities and various approaches to establishing such inequalities.

How to cite

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Roytwarf, N., and Yomdin, Yosef. "Bernstein classes." Annales de l'institut Fourier 47.3 (1997): 825-858. <http://eudml.org/doc/75246>.

@article{Roytwarf1997,
abstract = {One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes $R$. We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions. We present in detail various properties of the classes of functions, satisfying Bernstein type inequalities and various approaches to establishing such inequalities.},
author = {Roytwarf, N., Yomdin, Yosef},
journal = {Annales de l'institut Fourier},
keywords = {Bernstein inequality; algebraic functions; Taylor coefficients},
language = {eng},
number = {3},
pages = {825-858},
publisher = {Association des Annales de l'Institut Fourier},
title = {Bernstein classes},
url = {http://eudml.org/doc/75246},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Roytwarf, N.
AU - Yomdin, Yosef
TI - Bernstein classes
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 3
SP - 825
EP - 858
AB - One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes $R$. We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions. We present in detail various properties of the classes of functions, satisfying Bernstein type inequalities and various approaches to establishing such inequalities.
LA - eng
KW - Bernstein inequality; algebraic functions; Taylor coefficients
UR - http://eudml.org/doc/75246
ER -

References

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