Let {xn}nâˆˆN be a sequence of [0, 1] , {Î»n}nâˆˆN a sequence of positive real numbers converging to 0, and Î´ > 1. The classical ubiquity results are concerned with the computation of the Hausdorffâ€¦ (More)

We present an algorithm able to estimate the pointwise HÃ¶lder exponent of any function. This algorithm is based on a study of the wavelet decomposition of the function and is motivated by theâ€¦ (More)

We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns outâ€¦ (More)

We are interested in two properties of real numbers: the first one is the property of being well-approximated by some dense family of real numbers {xn}nâ‰¥1, such as rational numbers and more generallyâ€¦ (More)

In [10], new functional spaces, denoted K â€² x0 , were introduced. These spaces characterize the fine local regularity of functions, much in the spirit of 2-microlocal spaces C â€² x0 . In contrast withâ€¦ (More)

This work focuses on the local HÃ¶lder exponent as a measure the regularity of a function around a given point. We investigate in detail the structure and the main properties of the local HÃ¶lderâ€¦ (More)

We show how a joint multifractal analysis of a collection of signals unravels correlations between the locations of their pointwise singularities. The multivariate multifractal formalism,â€¦ (More)