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2000 | 141 | 3 | 209-219
Tytuł artykułu

Polynomial inequalities on algebraic sets

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give an estimate of Siciak's extremal function for compact subsets of algebraic varieties in $ℂ^n$ (resp. $ℝ^n$). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.
Czasopismo
Rocznik
Tom
141
Numer
3
Strony
209-219
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-06-24
poprawiono
2000-02-29
Twórcy
autor
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
autor
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
  • [Ba] M. Baran, Markov inequality on sets with polynomial parametrization, Ann. Polon. Math. 60 (1994), 69-79.
  • [BaPl1] M. Baran and W. Pleśniak, Markov's exponent of compact sets in $ℂ^n$, Proc. Amer. Math. Soc. 123 (1995), 2785-2791.
  • [BaPl2] M. Baran and W. Pleśniak, Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves, Studia Math. 125 (1997), 83-96.
  • [BaPl3] M. Baran and W. Pleśniak, Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities, this issue, 221-234.
  • [BLMT1] L. Bos, N. Levenberg, P. Milman and B. A. Taylor, Tangential Markov inequalities characterize algebraic submanifolds of $ℝ^N$, Indiana Univ. Math. J. 44 (1995), 115-138.
  • [BLMT2] L. Bos, N. Levenberg, P. Milman and B. A. Taylor, Tangential Markov inequalities on real algebraic varieties, ibid. 47 (1998), 1257-1271.
  • [BLT] L. Bos, N. Levenberg and B. A. Taylor, Characterization of smooth, compact algebraic curves in $ℝ^2$, in: Topics in Complex Analysis, P. Jakóbczak and W. Pleśniak (eds.), Banach Center Publ. 31, Inst. Math., Polish Acad. Sci., Warszawa, 1995, 125-134.
  • [Bru] A. Brudnyi, A Bernstein-type inequality for algebraic functions, Indiana Univ. Math. J. 46 (1997), 93-116.
  • [FeNa1] C. Fefferman and R. Narasimhan, Bernstein's inequality on algebraic curves, Ann. Inst. Fourier (Grenoble) 43 (1993), 1319-1348.
  • [FeNa2] C. Fefferman and R. Narasimhan, On the polynomial-like behavior of certain algebraic functions, ibid. 44 (1994), 1091-1179.
  • [FeNa3] C. Fefferman and R. Narasimhan, A local Bernstein inequality on real algebraic varieties, Math. Z. 223 (1996), 673-692.
  • [Gen] L. Gendre, Inégalité de Markov tangentielle locale sur les courbes algébriques de $ℝ^n$, Université Paul Sabatier de Toulouse, preprint, 1998.
  • [Iz] S. Izumi, A criterion for algebraicity on analytic set germs, Proc. Japan Acad. Ser. A 68 (1992), 307-309.
  • [Jos] B. Josefson, On the equivalence between locally and globally polar sets for plurisubharmonic functions in $ℂ^n$, Ark. Mat. 16 (1978), 109-115.
  • [K] M. Klimek, Pluripotential Theory, Oxford Univ. Press, London, 1991.
  • [Ł] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, Basel, 1991.
  • [PaPl] W. Pawłucki and W. Pleśniak, Markov's inequality and $C^∞$ functions on sets with polynomial cusps, Math. Ann. 275 (1986), 467-480.
  • [Pl1] W. Pleśniak, Invariance of the L-regularity of compact sets in $ℂ^n$ under holomorphic mappings, Trans. Amer. Math. Soc. 246 (1978), 373-383.
  • [Pl2] W. Pleśniak, Compact subsets of $ℂ^n$ preserving Markov's inequality, Mat. Vesnik 40 (1988), 295-300.
  • [Pl3] W. Pleśniak, Recent progress in multivariate Markov inequality, in: Approximation Theory, In Memory of A. K. Varma (N. K. Govil et al., eds.), Marcel Dekker, New York, 1998, 449-464.
  • [RoYo] N. Roytwarf and Y. Yomdin, Bernstein classes, Ann. Inst. Fourier (Grenoble) 47 (1997), 825-858.
  • [Sa] A. Sadullaev, An estimate for polynomials on analytic sets, Math. USSR-Izv. 20 (1983), 493-502.
  • [Si1] J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322-357.
  • [Si2] J. Siciak, Extremal plurisubharmonic functions in $ℂ^n$, Ann. Polon. Math. 39 (1981), 175-211.
  • [Tou] J.-C. Tougeron, Idéaux de fonctions différentiables, Springer, Berlin, 1972.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv141i3p209bwm
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