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GeezerVison is showing mathworld.wolfram.com — Shift-Invariant Operator -- from Wolfram MathWorld

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Shift-Invariant Operator

A shift-invariant operator is an operator T which commutes with all shift operators E^a, so

TE^a=E^aT

for all real a in a field. Any two shift-invariant operators commute.

See also

Delta Operator, Heaviside Calculus, Shift Operator

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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 Operator

Cite this as:

Weisstein, Eric W. "Shift-Invariant Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Shift-InvariantOperator.html

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