Related papers: Decoupling estimates in Fourier analysis
We study decoupling theory for functions on $\mathbb{R}$ with Fourier transform supported in a neighborhood of short Dirichlet sequences $\{\log n\}_{n=N+1}^{N+N^{1/2}}$, as well as sequences with similar convexity properties. We utilize…
The goal of this expository paper is to provide an introduction to decoupling by working in the simpler setting of decoupling for the parabola over $\mathbb{Q}_p$. Over $\mathbb{Q}_p$, commonly used heuristics in decoupling are…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
We demonstrate two applications of Fourier decoupling theorems over non-Archimedean local fields to real-variable problems. These include short mean value estimates for exponential sums, canonical-scale mean value estimates for exponential…
If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost)…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely does solution counting in older partial progress on…
The purpose of this paper is to present some further applications of the general decoupling theory from [B-D1, 2] to certain diophantine issues. In particular, we concider mean value estimates relevant to the Bombieri-Iwaniec approach to…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of…
I address the current status of dynamical decoupling techniques in terms of required control resources and feasibility. Based on recent advances in both improving the theoretical design and assessing the control performance for specific…
Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They…
Recent developments in machine-learning based molecular fragment linking have demonstrated the importance of informing the generation process with structural information specifying the relative orientation of the fragments to be linked.…
We review recent advances towards the computation of string couplings. Duality symmetry, mirror symmetry, Picard-Fuchs equations, etc. are some of the tools.
Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
Recent research in machine learning has given rise to a flourishing literature on the quantification and decomposition of model uncertainty. This information can be very useful during interactions with the learner, such as in active…