超可微函数空间ε_*和D_*中的乘法和卷积运算

利用Fourier-Laplace变换对ω-超可微函数空间ε_*(R~N)和ω-试验函数空间D*(R~N)中的乘法和卷积运算进行了讨论,并且证明了D(R~N)是D*(R~N)的乘子空间,在卷积意义下D(R~N)是ε_*(R~N)的乘子空间,且在D*(R~N)中Parseval等式成立.

Multiplications and Convolutions in Ultradifferentiable Function Spaces ε_* and D_*

In this paper,the multiplication and convolution of functions in theω- ultradifferentiable function spaces ε_*(R~N)andω-test function spaces D*(R~N)are dis- cussed,and it is obtained that D(R~N)is the multiplier space of D*(R~N),D(R~N)is the multiplier space of ε_*(R~N)in the sense of convolution,and the Parseval equation holds in the spaces of D*(R~N).