Markov's inequality: Sharpness, renewal theory, finite samples, reliability theory

It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in CN. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in CN, depend analytically on the generating polynomials, in the sense of the theory of analytic set-valued functions. It is also proved that every pluriregular set can be approximated by composite Julia sets. Finally, iteration of infinitely many polynomial mappings is used to give examples of pluriregular sets which are not composite Julia sets and on which Markov’s inequality fails.

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Sharpness conditions in multidimensional analogs of V. A. Markov’s inequality

Mathematical Notes ◽

10.1007/s11006-006-0214-4 ◽

2006 ◽

Vol 80 (5-6) ◽

pp. 893-897 ◽

Cited By ~ 1

Author(s):

V. I. Skalyga

Keyword(s):

Markov's Inequality ◽

Markov’S Inequality

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Constants in V.A. Markov’s inequality in Lp norms

Journal of Approximation Theory ◽

10.1016/j.jat.2014.12.010 ◽

2015 ◽

Vol 194 ◽

pp. 27-34 ◽

Cited By ~ 2

Author(s):

Grzegorz Sroka

Keyword(s):

Lp Norms ◽

Markov's Inequality ◽

Markov’S Inequality

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Bernstein and Markov-type inequalities for polynomials on real Banach spaces

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004102006217 ◽

2002 ◽

Vol 133 (3) ◽

pp. 515-530 ◽

Cited By ~ 8

Author(s):

GUSTAVO A. MUÑOZ ◽

YANNIS SARANTOPOULOS

Keyword(s):

Banach Space ◽

Hilbert Space ◽

Banach Spaces ◽

Real Banach Space ◽

Real Hilbert Space ◽

Markov Type ◽

Markov's Inequality ◽

Markov’S Inequality ◽

Derivatives Of ◽

Derivative Of A Polynomial

In this work we generalize Markov's inequality for any derivative of a polynomial on a real Hilbert space and provide estimates for the second and third derivatives of a polynomial on a real Banach space. Our result on a real Hilbert space answers a question raised by L. A. Harris in his commentary on problem 74 in the Scottish Book [20]. We also provide generalizations of previously obtained inequalities of the Bernstein and Markov-type for polynomials with curved majorants on a real Hilbert space.

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