In the present paper, we give sufficient conditions in order to establish the extension of the strong asymptotics up to the boundary and inside the unit disk for Sobolev orthogonal polynomials. We consider the following Sobolev inner product on the unit circle: with tt0 a finite positive Borel mea
Extension inside the disk of asymptotics for Sobolev orthogonal polynomials
β Scribed by E. Berriochoa; A. Cachafeiro
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 513 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
Let {Sn}n denote a sequence of polynomials orthogonal with respect to the Sobolev inner product where ΒΏ 0 and {d 0; d 1} is a so-called coherent pair with at least one of the measures d 0 or d 1 a Jacobi measure. We investigate the asymptotic behaviour of Sn(x), for n β +β and x ΓΏxed, x β C \ [ -1;
We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form x Ξ³ e -Ο(x) , with Ξ³ > 0, which include as particular cases the counterparts of the so-called Freud (i.e., when Ο has a polyn