In[]:=
Refine[Convolve[UnitBox[y/T],UnitBox[y/T],y,t],​​Assumptions->T>0]
Out[]=
-t-T
t>0&&t+T<0
t-T
t<0&&t>T
T
t0
-t+T
t>0&&t<T
t+T
t<0&&t+T>0
0
True
In[]:=
Refine[Convolve[UnitBox[y/a],UnitBox[y/a],y,t],​​Assumptions->a>0]
Out[]=
a-t
t>0&&a>t
a+t
a+t>0&&t≤0
0
True