Related papers: Localization and dimension free estimates for maxi…

Dynamical locality is a condition on a locally covariant physical theory, asserting that kinematic and dynamical notions of local physics agree. This condition was introduced in [arXiv:1106.4785], where it was shown to be closely related to…

The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

The aim of the paper is twofold. Firstly, we give an axiomatic presentation of Donaldson-Thomas theory for categories of homological dimension at most one with potential. In particular, we provide rigorous proofs of all standard results…

We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroes or maxima, their number, as well as their distribution…

Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…

N\"orlund strong logarithmic means of double Fourier series acting from space $% L\log L(\mathbb{T}^{2}) $ into space $L_{p}(\mathbb{T}% ^{2}), 0<p<1$ are studied. The maximal Orlicz space such that the N\"o% rlund strong logarithmic means…

We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry…

Let $\mathcal{L}$ be a fixed $d$-dimensional lattice. We study the localization properties of solutions of the stationary Schr\"odinger equation with a positive $L^\infty$ potential on tori $\mathbb{R}^d/L\mathcal{L}$ in the limit, as…

Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…

We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it…

We prove new bilinear estimates for the X^{s, b}_\pm(R^2) spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on R^{1+1}. The proof of the bilinear estimates follows from a…

The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We…

We develop a new formulation of well localized operators as well as a new proof for the necessary and sufficient conditions to characterize their boundedness between $L^2(\mathbb{R}^n,u)$ and $L^2(\mathbb{R}^n,v)$ for general Radon measures…

We prove some fundamental properties of mu-differentiable functions. A new notion of local minimizer and maximizer is introduced and several extremum conditions are formulated using the language of nonstandard analysis.

We study the \emph{upper regularity dimension} which describes the extremal local scaling behaviour of a measure and effectively quantifies the notion of \emph{doubling}. We conduct a thorough study of the upper regularity dimension,…

We deal with the problem of numerically computing the dual norm, which is important to study sparsity-inducing regularizations (Jenatton et al. 2011,Bach et al. 2012). The dual norms find application in optimization and statistical…

We show well-posedness of the $p$-Laplace evolution equation on $\mathbb{R}^d$ with square integrable random initial data for arbitrary $1<p<\infty$ and arbitrary space dimension $d\in\mathbb{N}$. The noise term on the right-hand side of…

We study the classic mechanism design problem of locating a public facility on a real line. In contrast to previous work, we assume that the agents are unable to fully specify where their preferred location lies, and instead only provide…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…