Let S-n[f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of S-n[f] and discuss the speed of the convergence of S-n[f] in weighted L-p space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial L-n[f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x) = e(-(1/2)alpha2) is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold: parallel to (S-n[f] - f)((k))Wu(b)parallel to (LP(R)) less than or equal to C (1/rootn)(r-k) parallel tof((r))Wu(B)parallel to (Lp(R)) and parallel to (L-n[f] - f)((k))Wu(b)parallel to (Lp(R)) less than or equal to C (1/rootn)(r-k) parallel tof((r))W(1+x(2))(r/3)u(B)parallel to (LP(R)), where u(gamma)(x) = (1 + \x \)(gamma), gamma epsilon R and k = 0,1,2...,r. (C) 2001 Elsevier Science B.V. All rights reserved.

- Publisher
- ELSEVIER SCIENCE BV

- Issue Date
- 2001-08

- Language
- English

- Article Type
- Article; Proceedings Paper

- Keywords
MEAN CONVERGENCE; SUFFICIENT CONDITIONS; LAGUERRE SERIES; HERMITE; INEQUALITIES; POLYNOMIALS

- Citation
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.133, no.1-2, pp.445 - 454

- ISSN
- 0377-0427

- Appears in Collection
- MA-Journal Papers(저널논문)

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