High Quality Content by WIKIPEDIA articles! The Kramers–Kronig relations are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane. These relations are often used to calculate the real part from the imaginary part (or vice versa) of response functions in physical systems because causality implies the analyticity condition is satisfied, and conversely, analyticity implies causality of the corresponding physical system. The relation is named in honor of Ralph Kronig and Hendrik Anthony Kramers.