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Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions
(Elsevier B.V., 2009-12-01)
We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.
Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions
(Elsevier B.V., 2009-12-01)
We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.
Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions
(Elsevier B.V., 2014)
Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives
(2011-11-01)
In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect ...
Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives
(2011-11-01)
In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect ...
MONOTONICITY AND ASYMPTOTICS OF ZEROS OF LAGUERRE-SOBOLEV-TYPE ORTHOGONAL POLYNOMIALS OF HIGHER ORDER DERIVATIVES
(Amer Mathematical SocProvidenceEUA, 2011)
Landau and Kolmogoroff type polynomial inequalities II
(2004-06-01)
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 ...
Landau and Kolmogoroff type polynomial inequalities II
(2004-06-01)
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 ...
Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials
(Elsevier B.V., 2003-04-01)
Let C-n(lambda)(x), n = 0, 1,..., lambda > -1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal. in (-1, 1) with respect to the weight function (1 - x(2))(lambda-1/2). Denote by X-nk(lambda), k = 1,....,n, the ...