Landau and Kolmogoroff type polynomial inequalities II - De Andrade, Eliana X.L. [UNESP]; Dimitrov, Dimitar K. [UNESP]; De Sousa, Lisandra E. [UNESP] (My University, 2004)
Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.
Keywords: Bessel polynomials; Extremal polynomials; Jacobi polynomials; Laguerre polynomials; Landau and Kolmogoroff type inequalities; Markov's inequality; Rayleigh-Ritz theorem