A shift-invariant operator is an operator 
which commutes with all shift
operators 
,
so
 |
for all real 
in a field. Any two shift-invariant operators commute.
Shift-Invariant Operator
See also
Delta Operator, Heaviside Calculus, Shift OperatorExplore with Wolfram|Alpha
References
Rota, G.-C.; Kahaner, D.; Odlyzko, A. "On the Foundations of Combinatorial Theory. VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.Referenced on Wolfram|Alpha
Shift-Invariant OperatorCite this as:
Weisstein, Eric W. "Shift-Invariant Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Shift-InvariantOperator.html