| Abstract: | In this paper, multiparameter eigenvalue (MPE) problems for matrices are considered. The notion of Jordan vector semilattices as a generalization of the notion of Jordan vector chains is introduced for a multiple spectrum point of disconnected MPE problems. The notion of generating vector is introduced. For the linear case, a special form of equations determining Jordan vector semilattices is presented. The above notions are extended to the case of connected MPE problems, including linear ones. The relationship between the Jordan vector semilattices of a connected linear MPE problem and the Jordan vector chains of the corresponding simultaneous spectral problems for matrices is established. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 219, 1994, pp. 213–220. This paper was supported by the Russian Foundation of Fundamental Research (grant 94-01-00919). Translated by V. B. Khazanov. |
