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Lipschitz conditions and lacunarity

Published online by Cambridge University Press:  09 April 2009

R. E. Edwards
R. E. Edwards
Affiliation:
Department of Mathematics Institute of Advanced Studies Australian National University
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We consider 2π-periodic functions on the limits and give simple and complete characterizations, in terms of Fourier coefficients, of functions which belong to various Lipschitz classes and whose Fourier series are lacunary. Such characterisations seem to be missing from the literature, though there are various wellknown partial characterisations valid for functions with arbitrary spectra; cf. the remarks following Theorem 1. The results given below form complements to and sharpenings of some of the standard results valid for the special case of lacunary series.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 272 - 277
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Edwards, R. E., Fourier Series: A Modern Introduction, Vols. I, II (Holt, Rinehart and Winston, Inc., New York, 1967).Google Scholar
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