Resolvent estimates for singularly perturbed elliptic operators in Holder spaces

The norm of the inverse operator of epsilon A + B - lambda I between the Besov spaces B-infinity,infinity(s)(Omega) and B-infinity,infinity(t)(Omega) is estimated, where A and B are uniformly elliptic operators with smooth coefficients and Dirichlet boundary conditions, A is of order 2m, B of order 2m', m > m'. The estimate holds for negative t. The Besov space B-infinity,infinity(s)(Omega) reduces to the space of Holder continuous functions C-s (<(Omega)over bar>) if s > 0 is non-integer. In particular, is shown A(epsilon) generates an analytic semigroup in B-infinity,infinity(s)(Omega), s is an element of (-1,0), if Omega = R(n) or R(+)(n) and A, B are constant coefficient operators without lower terms.