We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

Krein space operator-theoretic methods are used to prove that the operator (sgn x) d is similar to a selfadjoint operator in the Hilbert space L2 (R) . Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = )wu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem i...

On the basis of Sz. Nagy-Foia\c{s}-Langer and von Neumann-Wold decompositions, two decompositions for dissipative linear relations are given they realized by transforming invariant subspaces contractions, means Z transform. These permit separation selfadjoint completely nonselfadjoint parts a relation.