The Zygmund condition for polygonal approximation

Newman, D. J.

doi:10.1090/S0002-9939-1974-0361553-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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The Zygmund condition for polygonal approximation
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by D. J. Newman

Proc. Amer. Math. Soc. 45 (1974), 303-304

DOI: https://doi.org/10.1090/S0002-9939-1974-0361553-X

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Abstract:

We investigate the class of functions which can be uniformly approximated to within $O(1/n)$ by a canonical choice of piecewise ($n$-piece) linear functions. The class turns out identical to the Zygmund class.

References

Franklin Richards, On the saturation class for spline functions, Proc. Amer. Math. Soc. 33 (1972), 471–476. MR 294958, DOI 10.1090/S0002-9939-1972-0294958-4