Generalized functions associated with self-adjoint operators

In this paper, from several commutative self-adjoint operators on a Hilbert space, we define a class of spaces of fundamental functions and generalize d functions, which are characterized completely by selfadjoint operators. S pecially, using the common eigenvectors of these self-adjoint operators, we give the general form of expansion in series of generalized functions. 200 0 Mathematics subject classification: primary 4SF05, 47B25.