Related papers: Regularity properties of random wavelet series
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
In this paper we investigate the problem of learning an unknown bounded function. We be emphasize special cases where it is possible to provide very simple (in terms of computation) estimates enjoying in addition the property of being…
We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic…
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…
In this work, we prove that certain L^2-unbounded transformations of orthogonal wavelet bases generate vaguelets. The L^2-unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We…
Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for…
We study the law of random self-similar series defined above an irrational rotation on the Circle. This provides a natural class of continuous singular non-Rajchman measures.
In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise…