Weighted approximation for Erdðs weights
| dc.contributor.author | Damelin, Steven Benjamin | |
| dc.date.accessioned | 2017-03-01T12:45:12Z | |
| dc.date.available | 2017-03-01T12:45:12Z | |
| dc.date.issued | 1995 | |
| dc.description.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. | en_ZA |
| dc.description.librarian | MN (2017) | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/10539/22133 | |
| dc.language.iso | en | en_ZA |
| dc.title | Weighted approximation for Erdðs weights | en_ZA |
| dc.type | Thesis | en_ZA |
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