TOPICS
Search

Pincherle Derivative

The Pincherle derivative of an operator T is

T^'=Tx-xT,

where x:p(x)|->xp(x) is the operator of multiplication by x. If T is a shift-invariant operator, then its Pincherle derivative is also a shift-invariant operator.

Explore with Wolfram|Alpha

References

Pincherle, S. "Operatori lineari e coefficienti di fattoriali." Alti Accad. Naz. Lincei, Rend. Cl. Fis. Mat. Nat. (6) 18, 417-519, 1933.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

Pincherle Derivative

Cite this as:

Weisstein, Eric W. "Pincherle Derivative." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PincherleDerivative.html

Subject classifications