An **analytic semigroup** is a fundamental concept in functional analysis and the theory of semigroups of operators, particularly in the context of linear evolution equations. It pertains to a one-parameter family of bounded linear operators that have certain analytic properties.
Articles by others on the same topic
An analytic semigroup is a strongly continuous semigroup whose bounded-operator-valued extension is holomorphic in a sector about the positive time axis. Its infinitesimal generator of a semigroup satisfies for and, on each bounded time interval, . This estimate gives instantaneous spatial smoothing but creates an integrable-singularity question in an inhomogeneous variation-of-constants formula.