Improved decay of conical averages of the Fourier transform

定常可压缩锥形流的无限薄激波层解及基于傅里叶谱方法的数值结果

Infinite-thin shock layer solutions for stationary compressible conical flows and numerical results via Fourier spectral method

本文研究带攻角锥体的定常超声速流，构造含加权Dirac测度的无限薄激波层Radon测度解，推导奇异非线性ODE，并用傅里叶谱方法结合Newton法进行高精度数值求解。

The Fourier transform and the wave equation

We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Fourier transform.

带锥形奇点流形分析简介

A Short Introduction to the Analysis on Manifolds with Conical Singularities

本文是锥演算入门讲义，介绍带锥形奇点流形、Mellin 变换、锥 Sobolev 空间及椭圆性符号判据，并概述完整锥演算。

Wave front sets with respect to Banach spaces of ultradistributions. Characterisation via the short-time Fourier transform

We define ultradistributional wave front sets with respect to translation-modulation invariant Banach spaces of ultradistributions having solid Fourier image. The main result is their characterisation by the short-time Fourier transform.

On Fourier transforms of radial functions and distributions

We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier transform of any radial function $f(r)$ in any dimension, provided one knows the Fourier transform of the one-dimensional function $t\to f(|t|)$ and the two-dimensional function $(x_1,x_2)\to f(|(x_1,x_2)|)$. We prove analogous results for radial tempered distributions.

On the characterisations of wave front sets via the short-time Fourier transform

It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short paper we give complete characterisations of initial wave front sets via the short-time Fourier transform.