Necessary Conditions forLpConvergence of Lagrange Interpolation on an Arbitrary System of Nodes

✍ Scribed by Ying Guang Shi

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 394 KB
• Volume: 85
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0026

✦ Synopsis

This paper gives powerful necessary conditions for convergence of Lagrange interpolation on an arbitrary system of nodes in L p (d:) with d: belonging to the Szego 's class. This provides a partial answer to Problem XI of P. Tura n [J. Approx. Theory 29 (1980), 33 34]. It is shown that in this case the asymptotics of distribution of the nodes must behave like the power asymptotics.

1996 Academic Press, Inc.

with | n (x) :=| n (X, x) :=(x&x 1n )(x&x 2n ) } } } (x&x nn ), n=1, 2, ... . For simplicity sometimes we also write x k instead of x kn , etc.

Dealing with mean convergence of L n (X, f ) Tura n proposed [10, pp. 33 34] article no. 0026 16