Related papers: Mixed norm spaces and rearrangement invariant esti…
The aim of the paper is twofold. We establish refined Strichartz estimates for the Schr\"odinger equation on tori within the framework of partial regularity. As a result, we reveal that the solution of the free Schr\"odinger equation has…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
We extend the construction of Garsia-Rodemich spaces in different directions. We show that the new space \textbf{B,} introduced by Bourgain-Brezis-Mironescu \cite{bbm}, can be described via a suitable scaling of the Garsia-Rodemich norms.…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
In this paper we present the containment relationship between the spaces of analytic functions with average radial integrability RM(p,q) and a family of mixed norm spaces.
This paper addresses distributed consensus optimization problems with mixed-integer variables, with a specific focus on Boolean variables. We introduce a novel distributed algorithm that extends the Consensus Augmented Lagrangian…
In this paper we consider Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol'ski's, Besov's classes in the Lorentz space with the mixed norm.
In this paper we consider inhomogeneous Strichartz estimates in the mixed norm spaces which are given by taking temporal integration before spatial integration. We obtain some new estimates, and discuss about the necessary conditions.
This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
Inequality measures are quantitative measures that take values in the unit interval, with a zero value characterizing perfect equality. Although originally proposed to measure economic inequalities, they can be applied to several other…
We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a…
The present work aims to provide Meyers estimates throughout a finer inner regularity theory in perforated domains. We also provide a hypercontractivity property on correctors whenever the perforations are controlled with a uniformly…
We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the…
Sequential decision making under uncertainty is studied in a mixed observability domain. The goal is to maximize the amount of information obtained on a partially observable stochastic process under constraints imposed by a fully observable…
In this paper we study best \(m\)-term trigonometric approximation in weighted Wiener spaces and its consequences for Besov and Sobolev spaces with bounded mixed derivative/difference. We obtain several sharp asymptotic bounds for weighted…
We describe a framework for research and evaluation in Embodied AI. Our proposal is based on a canonical task: Rearrangement. A standard task can focus the development of new techniques and serve as a source of trained models that can be…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…