Necessary Conditions forLpConvergence of Lagrange Interpolation on an Arbitrary System of Nodes
Y. Shi
Apr 1, 1996
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Journal
Journal of Approximation Theory
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Key Takeaway Key Takeaway: This paper provides powerful necessary conditions for convergence of Lagrange interpolation on an arbitrary system of nodes in Lp(d) with d belonging to the Szego's class, providing a partial answer to Problem XI of P. Turan.
Abstract
Abstract This paper gives powerful necessary conditions for convergence of Lagrange interpolation on an arbitrary system of nodes in L p ( dα ) with dα belonging to the Szego's class. This provides a partial answer to Problem XI of P. Turan [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.
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