The value of the function is zero for all time$$outside the range.

$$

Let some other functions be defined by

$$

g$2[$n$]=$g$1[2$n$]$g$2[$n$]=-$g$1[2$n$]$

$$

g$3[$n$]=2$g$1[$n$2]$g$3[$n$]=2$g$1[$n$-2]$

$$

g$4[$n$]=3$g$1[$n$3]$