# Volterra operator

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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.

## Definition

The Volterra operator, V, may be defined for a function f  L2[0,1] and a value t  [0,1], as

${\displaystyle V(f)(t)=\int _{0}^{t}f(s)\,ds.}$

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## References

1. "Spectrum of Indefinite Integral Operators". Stack Exchange . May 30, 2012.
• Gohberg, Israel; Krein, M. G. (1970). Theory and Applications of Volterra Operators in Hilbert Space. Providence: American Mathematical Society. ISBN   0-8218-3627-7.