operatorsoften
Operatorsoften is a term used in some branches of functional analysis to describe a smoothing or regularization transformation applied to linear operators on function spaces. The basic idea is to modify an operator to reduce irregularities or high-frequency components while preserving essential structural properties of the original operator.
Formally, consider a Hilbert space H and a bounded operator T on H. An operatorsoften is implemented
Typical properties include that each O_eps(T) is a bounded operator if T is bounded, and the family
Examples and contexts include smoothing integral operators in L^2 spaces, where S_eps acts by convolution with