I know that

$$L({t}^{2})=\frac{2}{{s}^{3}}$$

but why is is that, if we use the convolution theorem for $1\ast {t}^{2}$, we get

$$L(1\ast {t}^{2})=\frac{1}{s}\ast \frac{2}{{s}^{3}}$$

Isn't $1\ast {t}^{2}$ equal to ${t}^{2}$?

$$L({t}^{2})=\frac{2}{{s}^{3}}$$

but why is is that, if we use the convolution theorem for $1\ast {t}^{2}$, we get

$$L(1\ast {t}^{2})=\frac{1}{s}\ast \frac{2}{{s}^{3}}$$

Isn't $1\ast {t}^{2}$ equal to ${t}^{2}$?