Space–time analyticity of weak solutions to linear parabolic systems with variable coefficients

Analytic smoothing properties of a general, strongly parabolic linear Cauchy problem of second order in RN×(0,T) with analytic coefficients (in space and time variables) are investigated. They are expressed in terms of holomorphic continuation of global (weak) L2-type solutions to the system. Given 00 are constants depending upon T′. The proof uses the extension of a solution to an L2-type solution in a domain in CN×C, such that this extension satisfies the Cauchy–Riemann equations. The holomorphic extension is thus obtained in a Hardy space H2. Applications include market completion by European options in Finance.