Shift Operator

DEFINITION 11.2.20 (Shift Operator)   A SHIFT OPERATOR, denoted by $E,$ is the operator which shifts the value at the next point with step $h,$ i.e.,

$$Ef(x)=f(x+h).$$

Thus,

$$Ey_i=y_{i+1}, \;\; E^2y_i=y_{i+2}, \;\; {\mbox{ and }} \;\; E^ky_i=y_{i+k}.$$