Poisson和公式在分数阶热方程中的应用

Applications of the Poisson Summation Formula to Fractional Heat Equations

本文利用Poisson和公式,证明了如下分数阶热方程(D_t~αlu=D_x^2u u(x1 0)=f(x))当f分别为周期函数和f∈S(■)时(速降函数空间),它们的热核满足关系H_t~α(x)=∑n=-∞H_t~α(x+n)进一步。

In this paper, we introduce fractional heat kernels, Hαt（x）, Hat（x） for fractional heatequation {Dαtu=D2xuu（x,0）=f（x） when f is periodic of period 1, and f ∈ S（R）, respectively. We get the relations between these two heat kernels： Hαt（x）=∞∑n=-∞ Hαt（x＋n）by using the Poisson summation formula. And analogous results hold for more general fractional differential equations.