On the generators of Clifford semigroups: Polynomial resolvents and their integral transforms

This paper deals with generators A of strongly continuous right linear semigroups in Banach two-sided spaces whose set scalars is an arbitrary Clifford algebra Cℓ(0,n). We study the invertibility operators form P(A), where P(x)∈R[x] any real polynomial, and we give integral representation for P(A)−1 by means a Laplace-type transform semigroup T(t) generated A. In particular, deduce new spherical quadratic resolvent (also called pseudoresolvent A). As immediate consequence, also obtain proof well-known