Markov inequality on sets with polynomial parametrization

Mirosław Baran

Annales Polonici Mathematici (1994)

  • Volume: 60, Issue: 1, page 69-79
  • ISSN: 0066-2216

Abstract

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The main result of this paper is the following: if a compact subset E of ℝ n is UPC in the direction of a vector v ∈ S n - 1 then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].

How to cite

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Mirosław Baran. "Markov inequality on sets with polynomial parametrization." Annales Polonici Mathematici 60.1 (1994): 69-79. <http://eudml.org/doc/262450>.

@article{MirosławBaran1994,
abstract = {The main result of this paper is the following: if a compact subset E of $ℝ^n$ is UPC in the direction of a vector $v ∈ S^\{n-1\}$ then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].},
author = {Mirosław Baran},
journal = {Annales Polonici Mathematici},
keywords = {extremal function; Markov inequality; UPC sets; uniformly polynomially cuspidal},
language = {eng},
number = {1},
pages = {69-79},
title = {Markov inequality on sets with polynomial parametrization},
url = {http://eudml.org/doc/262450},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Mirosław Baran
TI - Markov inequality on sets with polynomial parametrization
JO - Annales Polonici Mathematici
PY - 1994
VL - 60
IS - 1
SP - 69
EP - 79
AB - The main result of this paper is the following: if a compact subset E of $ℝ^n$ is UPC in the direction of a vector $v ∈ S^{n-1}$ then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].
LA - eng
KW - extremal function; Markov inequality; UPC sets; uniformly polynomially cuspidal
UR - http://eudml.org/doc/262450
ER -

References

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  1. [B1] M. Baran, Bernstein type theorems for compact sets in ℝ n , J. Approx. Theory 69 (1992), 156-166. Zbl0748.41008
  2. [B2] M. Baran, Complex equilibrium measure and Bernstein type theorems for compact sets in ℝ n , Proc. Amer. Math. Soc., to appear. 
  3. [B3] M. Baran, Plurisubharmonic extremal function and complex foliation for a complement of a convex subset of ℝ n , Michigan Math. J. 39 (1992), 395-404. 
  4. [B4] M. Baran, Bernstein type theorems for compact sets in ℝ n revisited, J. Approx. Theory, to appear. 
  5. [C] E. W. Cheney, Introduction to Approximation Theory, New York, 1966. Zbl0161.25202
  6. [G] P. Goetgheluck, Inégalité de Markov dans les ensembles effilés, J. Approx. Theory 30 (1980), 149-154. Zbl0457.41015
  7. [PP1] W. Pawłucki and W. Pleśniak, Markov’s inequality and C ∞ functions with polynomial cusps, Math. Ann. 275 (1986), 467-480. Zbl0579.32020
  8. [PP2] W. Pawłucki and W. Pleśniak, Extension of C ∞ functions from sets with polynomial cusps, Studia Math. 88 (1989), 279-287. Zbl0778.26010
  9. [P] W. Pleśniak, Markov’s inequality and the existence of an extension operator for C ∞ functions, J. Approx. Theory 61 (1990), 106-117. Zbl0702.41023
  10. [S] J. Siciak, Extremal plurisubharmonic functions in ℂ n , Ann. Polon. Math. 39 (1981), 175-211. Zbl0477.32018
  11. [Z] M. Zerner, Développement en série de polynômes orthonormaux des fonctions indéfiniment différentiables, C. R. Acad. Sci. Paris 268 (1969), 218-220. Zbl0189.14601

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