SEPARABILITY PROPERTIES OF CONVOLUTION-DIFFERENTIAL OPERATOR EQUATIONS IN WEIGHTED <i>L_p</i> SPACES

Abstract

In the present paper, separability properties of convolution - differential operator equations with unbounded operator coefficients in Banach space-valued weighted L-p-class are investigated. The coercive estimate for resolvent of the corresponding realization operator, especially its R - positivity is obtained. Finally, these results an applied to establish well-posedeness of the Cauchy problem for the abstract parabolic convolution equations and system of finite and infinite order integro-differential equations.