MINIMAL NORMALIZATION OF WIENER-HOPF OPERATORS IN SPACES OF BESSEL POTENTIALS

A class of operators is investigated which results from certain bounda ry and transmission problems, the so-called Sommerfeld diffraction pro blems. In various cases these are of normal type but not normally solv able, and the problem is how to normalize the operators in a physicall y relevant way, i.e., not loosing the Hilbert space structure of funct ion spaces defined by a locally finite energy norm. The present approa ch solves this question rigorously for the case where the lifted Fouri er symbol matrix function is Holder continuous on the real line with a jump at infinity. It incorporates the intuitive concept of compatibil ity conditions which is known from some canonical problems. Further it presents explicit analytical formulas for generalized inverses of the normalized operators in terms of matrix factorization. (C) 1998 Acade mic Press.