Volterra kernel

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A (matrix) function $K(s,t)$ of two real variables $s,t$ such that either $K(s,t)\equiv0$ if $a\leq s<t\leq b$ or $K(s,t)\equiv0$ if $a\leq t<s\leq b$. If such a function is the kernel of a linear integral operator, acting on the space $L_2(a,b)$, and is itself square-integrable in the triangle in which it is non-zero, the operator generated by it is known as a Volterra integral operator (cf. Volterra operator).


See also Volterra equation.

How to Cite This Entry:
Volterra kernel. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Bakushinskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article