Related papers: Decoupling inequalities for short generalized Diri…
Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy type Dirichlet forms are studied. When the range of jumps is finite our results are natural extensions to the corresponding ones derived earlier for diffusion…
We consider the problem of finding the Discrete Fourier Transform (DFT) of $N-$ length signals with known frequency support of size $k$. When $N$ is a power of 2 and the frequency support is a spectral set, we provide an $O(k \log k)$…
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 that shearlet systems yield superior $N$-term approximation rates compared with wavelet systems of functions whose first or higher order derivatives are smooth away from smooth discontinuity curves. We will also provide an…
Dualities between quantum field theories have proven to be a powerful tool in various areas of physics. In this paper, we introduce a new perspective for obtaining strong coupling expansions based on a well-known technique -- the…
Asymptotic expansions as well as necessary and sufficient conditions are provided for the pointwise convergence of the spherical partial integrals of the associated Fourier transforms on the real hyperbolic space. The proposed method…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…
We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, that are currently used to prove explicitly the existence of weak solutions to functional equations. We describe…
We study metric Diophantine approximation in local fields of positive characteristic. Specifically, we study the problem of improving Dirichlet's theorem in Diophantine approximation and prove very general results in this context.
We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detailed information about their geometry, and the percolative…
Breakthrough work of Bourgain, Demeter, and Guth recently established that decoupling inequalities can prove powerful results on counting integral solutions to systems of Diophantine equations. In this note we demonstrate that in…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
We consider the decoupling theory of a broad class of $C^5$ surfaces $\mathbb{M} \subset \mathbb{R}^3$ lacking planar points. In particular, our approach also applies to surfaces which are not graphed by mixed homogeneous polynomials. The…
We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz norms), tail…