中性卷积e_-^(λχ)(?)e_+^(μχ)

The Neutrix Convolution Product e_-^(λχ)ɑ(?)e_+^(μχ)

设f和g是D'内的广义函数,f_n(x)=f(x)r_n(x),当n→∞时,r_n(x)收敛于恒等函数。则中性卷积fg定义为序列{f_n*g}的极限,若极限h存在,即中性极限 N(f_n*g,φ)=(h,φ),(φ∈D)存在。在这篇文章中计算出了中性卷积e_-^(λx)e_+^(μx)和e_+^(μx)e_-^(λx)。利用这两个中性卷积又推出了一些其它的中性卷积。

Let f and g be distributions in D' and let f_n(x)=f(x)τ_n(x), where τ_n(x) is a certain function which converges to the identity function as n tends to infinity. Then the neutrix convolution product fg is defined as the neutrix limit of the sequence {f_n*g}, provided the limith exists in the sense that N—lim_(n-∞) (f_n*g, φ)=(h, φ) for all φ in D. The neutrix convolution products e_-^(λχ)e_+^(μχ) e_+^(μχ)e_-^(λχ) are evaluated, from which other neutrix convolution products are deduced.