Orthonormal polynomials with exponential-type weights
نویسندگان
چکیده
منابع مشابه
Derivatives of Orthonormal Polynomials and Coefficients of Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights
Let R −∞,∞ , and let Q ∈ C2 : R → 0,∞ be an even function. In this paper, we consider the exponential-type weights wρ x |x| exp −Q x , ρ > −1/2, x ∈ R, and the orthonormal polynomials pn w2 ρ;x of degree n with respect to wρ x . So, we obtain a certain differential equation of higher order with respect to pn w2 ρ;x and we estimate the higher-order derivatives of pn w2 ρ;x and the coefficients o...
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Orthogonal polynomials pn(W ; x) for exponential weights W 2 = e−2Q on a nite or in nite interval I , have been intensively studied in recent years. We discuss e orts of the authors to extend and unify some of the theory; our deepest result is the bound |pn(W ; x)|W (x)|(x − a−n)(x − an)|6C; x∈ I with C independent of n and x. Here a±n are the Mhaskar–Rahmanov–Sa numbers for Q and Q must satisf...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2008
ISSN: 0021-9045
DOI: 10.1016/j.jat.2007.12.004