- #1
mnb96
- 715
- 5
Hello,
I was wondering if there exists a (iso)morphism which preserves the operation of convolution, in respect to the pointwise-addition operation.
For example: it is well known that the Discrete Fourier Transform is a morphism which preserves convolution in respect to pointwise-multiplication:
[tex]F(f\ast g) = F(f)\cdot F(g)[/tex]
Is it possible to find another operator [tex]\mathcal{G}[/tex] (different than the FT) for which the following is valid?
[tex]\mathcal{G}(f\ast g) = \mathcal{G}(f)+\mathcal{G}(g)[/tex]
I was wondering if there exists a (iso)morphism which preserves the operation of convolution, in respect to the pointwise-addition operation.
For example: it is well known that the Discrete Fourier Transform is a morphism which preserves convolution in respect to pointwise-multiplication:
[tex]F(f\ast g) = F(f)\cdot F(g)[/tex]
Is it possible to find another operator [tex]\mathcal{G}[/tex] (different than the FT) for which the following is valid?
[tex]\mathcal{G}(f\ast g) = \mathcal{G}(f)+\mathcal{G}(g)[/tex]