IJPAM: Volume 40, No. 2 (2007)

NECESSARY CONDITIONS FOR $L^p$-CONVERGENCE
OF LAGRANGE INTERPOLATION IN FINITE DISC

Devendra Kumar
Department of Mathematics
D.S.M. Degree College
Kanth, 244501 (Moradabad), U.P., INDIA
e-mail: d_kumar001@rediffmail.com


Abstract.In this paper we have studied the powerful necessary conditions for convergence of Lagrange interpolation on an arbitrary system of nodes in $L^p(d\al)$ with $d\al$ belonging to the Szegö class. This provides a partial answer to Problem XI of P. Turàn, J. Approx. Theory, 29 (1980), 23-85, in finite disc.

Received: July 5, 2007

AMS Subject Classification: 30E10, 41A10

Key Words and Phrases: Lagrange interpolation polynomials, Borel measure, Szegö class

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 2