Although the star notation is widely used, it must be remembered that
convolution is an operator: At any *t* the value of *y(t)*
depends on the entire signals *x(t)* and *h(t)*. Thus, for
example, operations such as time shift must be treated carefully, since
*h(t - 2) * x(t - 2)* does NOT yield the signal
*y(t - 2)*.

Notice also that the mathematical operation * has an identity operation, since

for any (suitably continuous) signal *x(t)*.