In functional analysis, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces.
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.
The infinitesimal generator of a one-parameter semigroup T is an operator A defined on a possibly proper subspace of X as follows: The infinitesimal generator of a strongly continuous one-parameter semigroup is a closed linear operator defined on a dense linear subspace of X.
The Hille–Yosida theorem provides a necessary and sufficient condition for a closed linear operator A on a Banach space to be the infinitesimal generator of a strongly continuous one-parameter semigroup.