Related papers: Weighted restriction estimates and application to …
The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…
The purpose of these notes is describe the state of progress on the restriction problem in harmonic analysis, with an emphasis on the developments of the past decade or so on the Euclidean space version of these problems for spheres and…
Following the ideas from a paper by the same author, we prove abstract maximal restriction results for the Fourier transform. Our results deal mainly with maximal operators of convolution-type and $r-$average maximal functions. As a…
This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…
In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
In this paper, we are interested in the error estimates of the reiterated Stokes systems in a bounded $C^{1,1}$ domain with Dirichlet boundary conditions. And we have obtained the $O(\varepsilon)$ error estimates for the velocity term and…
The paper improves the accuracy of the one-dimensional fractional Fourier transform (FRFT) by leveraging closed Newton-Cotes quadrature rules. Using the weights derived from the Composite Newton-Cotes rules of order QN, we demonstrate that…
Sharp Strichartz estimates are proved for Schr\"odinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how…
In this paper, we present a proof of dispersive decay for both linear and nonlinear magnetic Schr\"odinger equations. To achieve this, we introduce the fractional distorted Fourier transforms with magnetic potentials and define the…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
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…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
We give an abstract argument that an a priori Fourier restriction estimate for a certain choice of exponents automatically implies maximal and variational Fourier restriction estimates. These, in turn, provide pointwise and quantitative…
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…
To resolve the non-convex optimization problem in partial wave analysis, this paper introduces a novel approach that incorporates fraction constraints into the likelihood function. This method offers significant improvements in both the…
Let $E\subset\rr$ be a closed set of Hausdorff dimension $\alpha$. We prove that if $\alpha$ is sufficiently close to 1, and if $E$ supports a probabilistic measure obeying appropriate dimensionality and Fourier decay conditions, then $E$…
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…
In this paper, we study the restriction estimate for a certain surface of finite type in $\mathbb{R}^3$, and partially improves the results of Buschenhenke-M\"{u}ller-Vargas. The key ingredients of the proof include the so called…
We show trilinear Strichartz estimates in one and two dimensions on frequency-dependent time intervals. These improve on the corresponding linear estimates of periodic solutions to the Schr\"odinger equation. The proof combines decoupling…
This article explores weighted $(L^p, L^q)$ inequalities for the Fourier transform in rank one Riemannian symmetric spaces of noncompact type. We establish both necessary and sufficient conditions for these inequalities to hold. To prove…