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Composition operator

In mathematics, the composition operator C ϕ {\displaystyle C_{\phi }} with symbol ϕ {\displaystyle \phi } is a linear operator defined by the rule C ϕ ( f ) = f ∘ ϕ {\displaystyle C_{\phi }(f)=f\circ \phi } where f ∘ ϕ {\displaystyle f\circ \phi } denotes function composition. It is also encountered in composition of permutations in permutation groups.

Applications, In holomorphic functional calculus & In Borel functional calculus