In mathematics, in the area of functional analysis and operator theory, the Volterra operator, named after Vito Volterra, is a bounded linear operator on the space L2[0,1] of complex-valued square-integrable functions on the interval [0,1].
On the subspace C[0,1] of continuous functions it represents indefinite integration.
It is the operator corresponding to the Volterra integral equations.
The Volterra operator, V, may be defined for a function f ∈ L2[0,1] and a value t ∈ [0,1], as[1]