Estimates of asymmetric Freud polynomials on the real line
نویسندگان
چکیده
منابع مشابه
Asymptotics of Derivatives of Orthogonal Polynomials on the Real Line
We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L2 norm. 1. Results Let μ be a nite positive Borel measure on [−1, 1] and let {pn}n=0 denote the corresponding orthonormal polynomials, so that ∫...
متن کاملCoeecients of Polynomials of Restricted Growth on the Real Line
Let : (?1; 1) ! (0; 1) be a given continuous even function and let m be a positive integer. We show that, with some additional restrictions on , there exist decreasing sequences x 1 ; : : :; x m and y 1 ; : : :; y m?1 of symmetrically located points on (?1; 1) and corresponding polynomials P and Q of degrees m ? 1 and m, respectively, satisfying jP(x)j (x) m ; jQ(x)j (x) m ; ? 1 < x < 1; where ...
متن کاملCoefficients of Polynomials of Restricted Growth on the Real Line
Let φ : (−∞,∞)→ (0,∞) be a given continuous even function and let m be a positive integer. We show that, with some additional restrictions on φ, there exist decreasing sequences x1, . . . , xm and y1, . . . , ym−1 of symmetrically located points on (−∞,∞) and corresponding polynomials P and Q of degrees m− 1 and m, respectively, satisfying |P (x)| ≤ φ(x), |Q(x)| ≤ φ(x), −∞ < x <∞, where equalit...
متن کاملZeros of orthogonal polynomials on the real line
Let pnðxÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppðdmÞ; we show there is a d40 so that for all n; either pn or pnþ1 has no zeros in ðE d;E þ dÞ: If E is an isolated point of suppðmÞ; we show there is a d so that for all n; either pn or pnþ1 has at most one zero in ðE d;E þ dÞ:We provide an example where the zeros of pn are dense in a gap of su...
متن کاملNew Integral Identities for Orthogonal Polynomials on the Real Line
Let be a positive measure on the real line, with associated orthogonal polynomials fpng and leading coe¢ cients f ng. Let h 2 L1 (R) . We prove that for n 1 and all polynomials P of degree 2n 2, Z 1 1 P (t) pn (t) h pn 1 pn (t) dt = n 1 n Z 1 1 h (t) dt Z P (t) d (t) : As a consequence, we establish weak convergence of the measures in the lefthand side. Orthogonal Polynomials on the real line, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1990
ISSN: 0021-9045
DOI: 10.1016/0021-9045(90)90105-y