Memory kernel ($(\kappa \ast v)(t)={\int }_0^t\kappa (u)v(t-u)du$)

A function weighting the influence of past values in a history-dependent equation. In a Volterra integral equation its convolution with the history is causal: only earlier times appear. For an integrable kernel, $\tilde{\kappa }(0)={\int }_0^{\infty }\kappa (u)du$ measures its response to a constant input. In a generalized Langevin equation, the friction memory kernel records delayed resistance to the velocity.