Céline Esser

Large deviation spectra based on wavelet leaders

We introduce a quantity that encapsulates the information given by the distribution at each scale of the wavelet leaders of a function, and which is independent of the chosen wavelet basis. This leads naturally to the definition of a new multifractal formalism which allows to detect non-concave multifractal spectra.

How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes

Abstract The Borel map j ∞ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. In the literature, it is well known that the restriction of j ∞ to the germs of quasianalytic ultradifferentiable classes which are strictly containing the real analytic functions can never be onto the corresponding sequence space. In this paper, we are interested in studying how large the image of j ∞ is and we investigate the size and the structure of this image by using different approaches (Baire residuality, prevalence and lineability). We give an answer to this question in the very general setting of quasianalytic ultradifferentiable classes defined by weight matrices, which contains as particular cases the classes defined by a single weight sequence or by a weight function.