Weighted approximation for Erdðs weights
Date
1995
Authors
Damelin, Steven Benjamin
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Abstract
We investigate Mean Convergence of Lagrange Interpolation and Rates of Approximation
for Erd5's Weights on the Real line.
An Erdg's Weight is of the form, W : • expI-Q]' where typically Q is even,
continuous and is of faster than polynomial growth at infinity.
Concerning Lagrange Interpolation, we obtain necessaryand sufficient conditions
for convergence in Lp (1::; p < 00) and in particular, sharp results for p > 4 and
1 <p < 4.
On Rates of Approximation, we first investigate the problem of formulating and
proving the correct Jackson Theorems for Erdifs Weights. This is accomplished in
Lp(O < p < 00) with endpoint effects in [-an, anI, the Mhaskar-Rahmanov-Saff interval.
We next obtain a net ural Realisation Functional for our class of weights and
prove its fundamental equivalence to our.modulus of continuity.
Finally, we prove the correct converse or Bernstein Theorems in Lp (0 < p :5 00)
and deduce a Marchaud Inequality for our modulus.