ON THE CHARACTERIZATION OF THE INTERMEDIATE SPACE IN GENERALIZED FACTORIZATIONS

The study of systems of singular integral equations of CAUCHY type, of TOEPLITZ and WIENER-HOPF operators leads to the question of existence and representation of generalized factorizations of matrix functions Phi in [L(p)(Gamma, rho)](m). This yields a corresponding factorizatio n of the basic multiplication or translation invariant operator A = A_ CA(+), respectively, which can be seen as a splitting of a bounded int o unbounded operators. The present paper is devoted to the study of th e nature of the induced intermediate space Z = im A(+) = im A_(-1), in particular, for Gamma = R and Phi is an element of G[C-beta(R)](m x m ) which is of special interest in certain applications. As we know, th is implies detailed results about the structure and the explicit asymp totic behaviour of solutions of boundary and transmission problems nea r singular points with a relation also to eigenvalue problems which re sult from the classical series expansion approach or from the MELLIN s ymbol calculus (see [13]).