论文标题
L^2个空间中的线性化玻尔兹曼操作员的光谱研究具有多项式和高斯重量
Spectral study of the linearized Boltzmann operator in L^2 spaces with polynomial and Gaussian weights
论文作者
论文摘要
本文的目的是扩展到l^2（r^d，（1+| v |）^2k dv）频谱研究由R. Ellis和M. Pinsky在L^2（r^d，Exp（| v |^2/2）dv）中，由空间上的空间上的空间不均匀地线性化的Boltzmann Operator for Hard Spheres for Hard Spheres。更准确地说，我们将傅立叶算子空间变量的傅立叶变换视为固定参数。然后，我们针对该操作员进行了一项针对小频率的精确研究（通过将其视为同质频率的扰动），并从光谱和半群观点的大频率进行了较大的频率。我们的方法基于线性操作员的扰动理论以及M.P.的扩大论点。 Gualdani，S。Mischler和C. Mouhot。
The aim of this paper is to extend to the spaces L^2(R^d , (1+|v|)^2k dv) the spectral study led in L^2(R^d , exp(|v|^2/2)dv) by R. Ellis and M. Pinsky on the space inhomogeneous linearized Boltzmann operator for hard spheres. More precisely, we look at the Fourier transform in the space variable of the inhomogeneous operator and consider the dual Fourier variable as a fixed parameter. We then perform a precise study of this operator for small frequencies (by seeing it as a perturbation of the homogeneous one) and also for large frequencies from spectral and semigroup point of views. Our approach is based on perturbation theory for linear operators as well as enlargement arguments from M.P. Gualdani, S. Mischler and C. Mouhot.
