A weak local irregularity property in S^\nu spaces

Although it has been shown that, from the prevalence point of view, the elements of the S^ \nu spaces are almost surely multifractal, we show here that they also almost surely satisfy a weak uniform irregularity property

A wavelet characterization for the upper global Holder index

In this paper, we give a wavelet characterization of the upper global Holder index, which can be seen as the irregular counterpart of the usual global Holder index, for which a wavelet characterization is well-known

ENSO forecast using a wavelet-based mode decomposition

We introduce a new method for forecasting major El Niño/ La Niña events based on a wavelet mode decomposition. This methodology allows us to approximate the ENSO time series with a superposition of three periodic signals corresponding to periods of about 31, 43 and 61 months respectively with time-varying amplitudes. This pseudo-periodic approximation is then extrapolated to give forecasts. While this last one only resolves the large variations in the ENSO time series, three years hindcast as retroactive prediction allows to recover most of the El Niño/ La Niña events of the last 60 years

Prevalence of ''nowhere analyticity''

This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study in Gevrey classes of functions

A refinement of the Snu-based multifractal formalism

In this work, we introduce a generalization of the Snu spaces underlying a multifractal formalism for non-concave spectra. We prove that the essential topological properties of the Snu spaces can be transposed in this context; in particular, these new spaces are metric. More importantly, we show that the associated multifractal formalism can detect the logarithmic correction in a Brownian motion resulting from the law of the iterated logarithm. We also build two families of multifractal functions with prescribed pointwise regularity and displaying a logarithmic correction in order to illustrate the usefulness of these generalized spaces

Functional spaces defined via Boyd functions

editorial reviewedIn this work, we present several generalized functional spaces, primarily the $T_p^u$ spaces, originally introduced in essence by Calderón and Zygmund through the lens of Boyd functions. We provide conditions that relate functions belonging to these spaces with their wavelet coefficients. Subsequently, we propose a multifractal formalism based on these spaces, which generalizes the so-called wavelet leaders method, and demonstrate that it holds on a prevalent set. We also consider potential applications to partial differential equations