 Volterra operator

The Volterra integration operator on $L^2([0,1])$ is compact and injective, but its inverse is differentiation and is unbounded. Its singular values $2/((2n-1)\pi )$ tend to zero, making recovery of a function from noisy indefinite-integral data an ill-posed inverse problem.

The Volterra operator is a type of integral operator that is commonly encountered in the study of functional analysis and integral equations. It is typically used to describe processes that can be modeled by integral transforms.