Abstract
In this paper, the B-separability properties of anisotropic convolution-operators are investigated. In particular, the sharp estimates for the resolvent are established. Thus these operators are positive and also are generators of analytic semigroups. Moreover, we find sufficient conditions that guarantee the maximal B-regularity of the Cauchy problem for a parabolic convolution equation. Finally, the convolution equation is applied to establish maximal regularity properties for an anisotropic integro-differential equations and their infinite systems.
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