In functional analysis, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction semigroups, with the general case being called the Feller–Miyadera–Phillips theorem (after William Feller, Isao Miyadera, and Ralph Phillips). The contraction semigroup case is widely used in the theory of Markov processes. In other scenarios, the closely related Lumer–Phillips theorem is often more useful in determining whether a given operator generates a strongly continuous contraction semigroup. The theorem is named after the mathematicians Einar Hille and Kōsaku Yosida who independently discovered the result around 1948.