Oscillating singularities and fractal functions (Q2715894)

In this paper, the authors summarize some of their results about oscillating singularities of fractal functions from two papers [J. Fourier Anal. Appl. 4, No.~2, 159-174 (1998; Zbl 0914.28005); J. Stat. Phys. 87, No.~1-2, 179-209 (1997; Zbl 0917.28007)]. They show that a singular behavior must be described by two exponents: the Hölder exponent \(h\) for the ``strength'' of the singularity, and the oscillation exponent \(\beta\) for quantifying the divergence of the instantaneous frequency. These two exponents can be characterized by using wavelet analysis. The authors introduce a new multifractal formalism to estimate the \(D(h, \beta)\) spectrum for a large class of fractal functions involving both cusp and oscillating singularities.NEWLINENEWLINEFor the entire collection see [Zbl 0911.00013].