New Characterizations of Ratio Asymptotics for Orthogonal Polynomials
β Scribed by Ying Guang Shi
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 93 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0021-9045
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β¦ Synopsis
In this paper some new characterizations of ratio asymptotics for orthogonal polynomials are given.
π SIMILAR VOLUMES
We prove that if both [P n (x)] n=0 and [{ r P n (x)] n=r are orthogonal polynomials for any fixed integer r 1, then [P n (x)] n=0 must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both [P n (x)] n=0 and [(dΓdx) r P n
Strong asymptotics for the sequence of monic polynomials Q n (z), orthogonal with respect to the inner product with z outside of the support of the measure + 2 , is established under the additional assumption that + 1 and + 2 form a so-called coherent pair with compact support. Moreover, the asympt
Ratio and relative asymptotics are given for sequences of polynomials orthogonal with respect to measures supported on an arc of the unit circle, where their absolutely continuous component is positive almost everywhere. The results obtained extend to this setting known ones given by Rakhmanov and M