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Shift Operator

A shift operator is an operator E such that

E^ap(x)=p(x+a).

The unit shift is implemented in the Wolfram Language as DiscreteShift[f[k], k], and the multiple shift of step h as DiscreteShift[f[k], {k, n, h}], giving f(k+nh).

See also

Shift-Invariant 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 Operator

Cite this as:

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

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