SECTORIAL OPERATORS WITH CONVOLUTION TERM

In the present paper, separability properties of convolution-differential equations with unbounded operator coefficients in Banach valued L-p spaces are investigated. A coercive estimate for resolvent of corresponding realization operator, especially, its R-sectoriality is obtained. Finally, these results applied to establish maximal regularity of Cauchy problem for the abstract parabolic convolution equations and integro-differential equations on infinite dimension state spaces.