7 Wavelet Methods for Pointwise Regularity
VII, we will use the same starting point and apply the wavelet charac-
terization of Chapter V in order to show that a(x) has, at the ratio-
nals which are ratios of two odd numbers, a trigonometric chirp where
a = 3/2, $ = 1 and r = 1/2.
Finally we will apply the results of Chapter VI to show that the
Riemann function has a logarithmic chirps of regularity 7 = 1/2 at
quadratic irrationals.
Some of these results have been announced in [20], [21], or [25].
Acknowledgements: The authors wish to thank A. Grossman and
B. Torresani for enriching discussions about chirps, and S. Fromm for
many remarks and comments on this text.
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