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Markov inequality on the graph of holomorphic function

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EN
Abstrakty
EN
The purpose of this paper is to show that the Markov inequality does not hold on the graph of holomorphic function.
Rocznik
Strony
58--64
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
autor
  • University of Agriculture in Krakow, Department of Applied Mathematics, Balicka 253c, 30-198 Kraków, Poland
Bibliografia
  • 1. R.P. Boas, Inequalities for the derivatives of polynomials, Mathematics Magazine, 1969, 42, 165-174.
  • 2. A.A. Markov, On a problem of D.I. Mendeleev (Russian), Zapishi Imp. Akad. Nauk, 1889, 62, 1-24.
  • 3. M. Baran, Bernstein Type Theorems for Compact Sets in Rn Revisited, J. Approx. Theory, 1994, 79 (2), 190-198.
  • 4. M. Baran, Markov inequality on sets with polynomial parametrization, Ann. Polon. Math., 1994, 60 (1), 69-79.
  • 5. M. Baran and W. Pleśniak, Markov's exponent of compact sets in Cn, Proc.Amer. Math. Soc., 1995, 123 (9), 2785-2791.
  • 6. M. Baran and W. Pleśniak, Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves, Studia Math., 1997, 125, 83-96.
  • 7. M. Baran and W. Pleśniak, Polynomial Inequalities on Algebraic Sets, Studia Math., 2000, 41 (3), 209-219.
  • 8. L. Białas-Cież, Markov Sets in C are not Polar. Bull. Pol. Acad. Sci., Math., 1998, 46(1), 83-89.
  • 9. L. Białas-Cież, Equivalence of Markov's property and Hölder continuity of the Green function for Cantor-type sets, East Journal on Approximations, 1995, 1(2), 249-253.
  • 10. L. Białas-Cież and A. Volberg, Markov's property of the Cantor ternary set, Studia Math., 1993, 104, 259-268.
  • 11. L. Białas-Cież and R. Eggink, L-regularity of Markov sets and of m-perfect sets in the complex plane. Constr. Approx., 2008, 27, 237-252.
  • 12. L. Bos, N. Levenberg, P. Milman and B.A. Taylor, Tangential Markov Inequalities Characterize Algebraic Submanifolds of RN, Indiana Univ. Math. Journal, 1995, 44 (1), 115-138.
  • 13. L. Bos and P. Milman, On Markov and Sobolev type inequalities on compact subsets in Rn, In "Topics in Polynomials in One and Several Variables and Their Applications" (Th. Rassias et al. eds.), World Scientific, Singapore (1992), 81-100.
  • 14. L. Bos and P. Milman, Sobolev-Gagliardo-Nirenberg and Markov type inequalities on subanalytic domains, Geometric and Functional Analysis, 1995, 5 (6), 853-923.
  • 15. W. Gautschi, "The Incomplete Gamma Functions Since Tricomi". In Tricomi's ideas and contemporary applied mathematics, Atti Convegni Lincei, Rome, 1998, pages 203-237.
  • 16. P. Goetgheluck, Inégalité de Markov dans les ensembles efillés, J. Approx. Theory, 1980, 30, 149-154.
  • 17. P. Goetgheluck, Polynomial Inequalities on General Subsets of RN , Colloq. Math., 1989, 57 (1), 127-136.
  • 18. P. Goetgheluck and W. Ple±niak, Counter-examples to Markov and Bernstein Inequalities, J. Approx. Theory, 1992, 69, 318-325.
  • 19. A. Goncharov, A compact set without Markov's property but with an extension operator for C1 functions, Studia Math., 1996, 119, 27-35.
  • 20. L.A. Harris, A Bernstein-Markov theorem for normed spaces, J. Math. Anal. Appl., 1997, 208, 476-486.
  • 21. A. Jonsson, Markov's inequality on compact sets, In: "Orthogonal Polynomials and Their Applications" (C. Brezinski, L. Gori and A. Ronveaux, eds.), 1991, 309-313.
  • 22. A. Jonsson, Markov's Inequality and Zeros of Orthogonal Polynomials on Fractal Sets, J. Approx. Theory, 1994, 78, 87-97.
  • 23. M. Klimek, Pluripotential Theory, Oxford Univ. Press, London, 1991.
  • 24. W. Pawłucki and W. Pleśniak, Markov's inequality and C1 functions on sets with polynomial cusps, Math. Ann., 1986, 275, 467-480.
  • 25. W. Pawłucki and W. Pleśniak, Extension of C1 functions from sets with polynomial cusps, Studia Math., 1988, 88, 279-287.
  • 26. R. Pierzchała, UPC condition in polynomially bounded o-minimal structures, J. Approx. Theory, 2005, 132, 25-33.
  • 27. W. Pleśniak, Compact subsets of Cn preserving Markov's inequality, Mat. Vesnik, 1988, 40, 295-300.
  • 28. W. Pleśniak, A Cantor regular set which does not have Markov's property, Ann. Polon. Math., 1900, 51, 269-274.
  • 29. W. Pleśniak, Markov's inequality and the existence of an extension operator for C1 functions, J. Approx. Theory, 1990, 61, 106-117.
  • 30. T. Ransford, Potential Theory in the Complex Plane. In: Lond. Math. Soc. Stud. Texts, vol. 28. Cambridge, 1995.
  • 31. J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc., 1962, 105, 322-357.
  • 32. J. Siciak, Highly noncontinuable functions on polynomially convex sets, Univ. Jagello. Acta Math., 1985, 25, 95-107.
  • 33. V. Totik, Markoff constants for Cantor sets, Acta Sci. Math. (Szeged), 1995, 60, 715-734.
  • 34. A. Volberg, An estimate from below for the Markov constant of a Cantor repeller, In: "Topics in Complex Analysis", eds. P. Jakóbczak and W.Pleśniak, Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences 31, 393-390.
  • 35. A. Zeriahi, Inégalités de Markov et développement en série de polynômes orthogonaux des fonctions C1 et A1, in: "Proceedings of the Special Year of Complex Analysis of the Mittag-Letter Institute 1987-88" (ed. J.F. Fornaess), Princeton Univ. Press, Princeton New Jersey, 1993, 693-701.
  • 36. M. Zerner, Développement en séries de polynômes orthonormaux des fonctions indéfiniment différentiables, C. R. Acad. Sci. Paris Sér. I, 1969, 268, 218-220.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-13747396-ecfc-423b-be65-a5b0dbc3c444
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