| Abstract: | For H^{ infty} functions whose radial limits are almost everywhere continuous on the unit circle in the complex plane, we give an estimate, in terms of the average modulus of continuity, for approximation using Lagrange interpolating, and more generally quasi-interpolating, polynomials at the nth roots of unity. Our error estimate not only improves the existing results on Lagrange interpolation using the uniform modulus of continuity, but also gives an estimation for the Motzkin-Sharma quasi-interpolatory polynomial approximation. Furthermore, our results can be easily modified to give error estimations for more general interpolatory processes such as the Hermite-Fejér interpolation. |
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