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Volterra operator

From Wikipedia, the free encyclopedia

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

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

Properties

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See also

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References

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  1. ^ Rynne, Bryan P.; Youngson, Martin A. (2008). "Integral and Differential Equations 8.2. Volterra Integral Equations". Linear Functional Analysis. Springer. p. 245.
  2. ^ a b c "Spectrum of Indefinite Integral Operators". Stack Exchange. May 30, 2012.
  3. ^ "Volterra Operator is compact but has no eigenvalue". Stack Exchange.

Further reading

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  • Gohberg, Israel; Krein, M. G. (1970). Theory and Applications of Volterra Operators in Hilbert Space. Providence: American Mathematical Society. ISBN 0-8218-3627-7.