On asymptotic properties of Laguerre–Sobolev type orthogonal polynomials
✍ Scribed by Molano, Luis Alejandro Molano
- Book ID
- 121696715
- Publisher
- Elsevier
- Year
- 2013
- Tongue
- English
- Weight
- 276 KB
- Volume
- 19
- Category
- Article
- ISSN
- 1319-5166
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📜 SIMILAR VOLUMES
In this paper we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-type inner product where p and q are polynomials with real coefficients, and A is a positive semidefinite matrix. We will focus our attention on their outer relative asymptotics with respect to the
Let {S,} denote the sequence of polynomials orthogonal with respect to the Sobolev inner product fo +°° f+°c :,. x . ,.x--%-X dx (f.g)s = f(x)o(x)x%-Xdx + 2 J ~ )9( )x . ## JO where ~ > -1, 2 > 0 and the leading coefficient of the S~ is equal to the leading coefficient of the Laguerre polynomial
In this report we will survey some of the main ideas and tools which appeared recently in the study of the analytic properties of polynomials orthogonal with respect to inner products involving derivatives. Although some results on weak asymptotics are mentioned, the strong outer asymptotics constit