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
Asymptotics of Laurent Polynomials of Odd Degree Orthogonal with Respect to Varying Exponential Weights
โ Scribed by K.T.R. McLaughlin; A.H. Vartanian; X. Zhou
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 813 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0176-4276
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๐ SIMILAR VOLUMES
We consider asymptotics for orthogonal polynomials with respect to varying exponential weights w n (x)dx = e -nV (x) dx on the line as n โ โ. The potentials V are assumed to be real analytic, with sufficient growth at infinity. The principle results concern Plancherel-Rotach-type asymptotics for the
We consider orthogonal polynomials {p n,N (x)} โ n=0 on the real line with respect to a weight w(x) = e -NV (x) and in particular the asymptotic behaviour of the coefficients a n,N and b n,N in the three-term recurrence For one-cut regular V we show, using the Deift-Zhou method of steepest descent