The analyticity of abstract parabolic and correct systems

摘要

Let A be the matrix associated with an abstract parabolic system in the sense of Shilov or correct system in the sense of Petrovskii. We show that if the spectrum of its symbol is contained in a sector including some negative real axis, then A generates an analytic regularized semigroup. The corresponding result related to numerical range conditions is also showed. Moreover, these results are applied to matrices of partial differential operators on many function spaces.