# Volterra kernel

From Encyclopedia of Mathematics

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).

#### Comments

See also Volterra equation.

**How to Cite This Entry:**

Volterra kernel.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Volterra_kernel&oldid=31953

This article was adapted from an original article by A.B. Bakushinskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article