DISTRIBUTION-THEORY FOR DISCONTINUOUS TEST FUNCTIONS AND DIFFERENTIAL-OPERATORS WITH GENERALIZED COEFFICIENTS

Investigation of the differential operators with the generalized coeff icients having singular support on a disjoint set of points requires t he consideration of the distribution theory with the set of discontinu ous test functions. Such a distribution theory for test functions havi ng discontinuity at one point is developed. A four-parameter family of Schrodinger operators, formed by the operators with singular potentia l, singular metrics and singular gauge field, is considered. It is pro ved that this family of singular interactions describes all possible s elfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point. Approximation by operators with smooth coefficients is discussed. (C) 1996 Academic Pr ess, Inc.