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.
LetA 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, thenA 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.
基金
This work was supported by the National Natural Science Foundation of China(Grant No. 19971031)
Fok Ying Tung Education Foundation, and the Foundation for Excellent Young Teachers of China.
