The spectrum of multiparameter problems in Hilbert space

Source abstract

Synopsis In this paper, appropriate definitions are given for the spectra of multiparameter problems in Hilbert space when the operators involved are not necessarily self-adjoint. Notions of adjoint multiparameter problems are introduced, and some properties of the spectrum of a single linear operator are generalised to multiparameter settings. The results which are achieved are compared with those in the literature which have beendeveloped for multiparameter problems involving self-adjoint operators.