We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e -Q(x) dx on the real line, where Q(x) = โ 2m k=0 q k x k , q 2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem
โฆ LIBER โฆ
Strong Asymptotics of Orthonormal Polynomials with the Aid of Green's Function
โ Scribed by Peherstorfer, Franz; Steinbauer, Robert
- Book ID
- 118200283
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2000
- Tongue
- English
- Weight
- 213 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0036-1410
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The polynomials P, and Q,~ having degrees n and m, respectively, with P, monic, that solve the approximation problem Pn(z)e -z + Qm(z) = C(z n+m+l ) will be investigated for their asymptotic behavior, in particular in connection with the distribution of their zeros. The symbol C means that the left-