Related papers: Improved decay of conical averages of the Fourier …

In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive…

We give conditions on a real-valued function $F$ on $\mathbb{Z}^d$, for $d>2$, which ensure that the solution $G$ to the convolution equation $(F*G)(x) = \delta_{0,x}$ has Gaussian decay $|x|^{-(d-2)}$ for large $|x|$. Precursors of our…

Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to…

We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge 4$.

The Fourier decay rate of a coin-tossing type measure is investigated. Explicit estimation is given. Our method relies upon a classical result of Hartman and Kershner. As an application, we present a new example of a measure whose Fourier…

This is a continuation of the paper "Restriction theorem for Fourier-Dunkl transform I: Cone surface, J. Pseudo-Differ. Oper. Appl. 14(1), Paper No. 5 (2023)", where the authors introduced and studied the Fourier-Dunkl transform on…

We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By calculating the Fourier transform of this generalized Dedekind…

We study bilinear $L^2$ Fourier restriction estimates which are related to the 2d wave equation in the sense that we restrict to subsets of thickened null cones. In an earlier paper we studied the corresponding 3d problem, obtaining several…

The decay rates and spectroscopy of the $D$ and $D_s$ mesons are computed in a nonrelativistic phenomenological quark-antiquark potential of the type $V(r)=-{4/3}\frac{\alpha_s}{r}+A r^{\nu}$ with different choices of $\nu$. Numerical…

We apply recent circle tangency estimates due to Pramanik--Yang--Zahl to prove sharp weighted Fourier extension estimates for the cone in $\mathbb{R}^3$ and $1$-dimensional weights. The idea of using circle tangency estimates to study…

Suppose $0 < \alpha \leq n$, $H: \Bbb R^n \to [0,1]$ is a Lebesgue measurable function, and $A_\alpha(H)$ is the infimum of all numbers $C$ for which the inequality $\int_B H(x) dx \leq C R^\alpha$ holds for all balls $B \subset \Bbb R^n$…

We study random variables of the form $f(X)$, when $f$ is a degree $d$ polynomial, and $X$ is a random vector on $\mathbb{R}^{n}$, motivated towards a deeper understanding of the covariance structure of $X^{\otimes d}$. For applications,…

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

In this paper, we study the average of shifted sum for general multiplicative functions. As applications, we prove non-trivial upper bounds for weighted averages of shifted convolutions involving $GL(2)$ and $GL(3)$ Fourier coefficients…

Can one characterise the Fourier decay of a product measure in terms of the Fourier decay of its marginals? We make inroads on this question by describing the Fourier spectrum of a product measure in terms of the Fourier spectrum of its…

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

Let $f(d)$ be the smallest value for which every bridgeless graph $G$ with diameter $d$ admits a strong orientation $\overrightarrow{G}$ such that the diameter of $\overrightarrow{G}$ is at most $f(d)$. Chv\'atal and Thomassen (1978)…

We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t)^{-1/4})$ in $L^2$ as…

An algebraic lower bound on the energy decay for solutions of the advection-diffusion equation in $\mathbb{R}^d$ with $d=2,3$ is derived using the Fourier splitting method. Motivated by a conjecture on mixing of passive scalars in fluids, a…

The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…