Volterra operator


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 of complex-valued square-integrable functions on the interval . On the subspace C of continuous functions it represents indefinite integration. It is the operator corresponding to the Volterra integral equations.

Definition

The Volterra operator, V, may be defined for a function fL2 and a value t ∈ , as

Properties