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).