ВЕСТНИК ВГУ, Серия физика, математика, 2002, ¹ 1 ON SOME QUESTIONS OF THE SPECTRAL THEORY OF LINEAR RELATIONS © 2002 г. <...> A. G. BASKAKOV, K. I. CHERNYSHOV* Voronezh State University *Voronezh State Forestry Academy § 1. <...> Introduction The present paper1 investigation of certain questions of the spectral theory of linear relations (multivalued linear operators) as well as to the construction of solutions of linear generalized differential equations in a Banach space with the help of degenerate semigroups of linear bounded operators. <...> At the same time the theory of linear relations is covered insufficiently in the Russian mathematical literature. <...> Let us draw attention to paper [3], in which linear relations on Hilbert space are considered. <...> Let us introduce principal notions of the is devoted to the () (DD )D+= ∩ () ( ( xy y z,∈ ,AB is called the product of linear relations XY Y ZAB Ч . <...> BA =, ∈xz X Z y D Y () ( , )∈ } of multivalued operator ° () 2Y where ° inverse relation with respect to A. Each linear relation XY AA AA Further they are identixx 2Y =∈ . theory of linear relations used below. <...> We do not adhere to the terminology of [1, 2] (for example, we avoid the notion of the multivalued linear operator) and consider linear relations on one Banach space, as usual. <...> Note =+ ∀ ∈ Ч, then it is called a closed linear relation. <...> The sets {|(yY x y∈, ∈ } yY x D∈∃ ∈ A such ) ,∈A from X is called the domain of ) A , linear relations from XY suppose that () ( X Y, fied and the same symbol A is used for their notation. <...> Let us denote by ()LR X Y, the set of closed Ч; if XY ) =, then we LO() of linear closed operators, acting from X to Y, is considered as a subspace of ()LR X Y LR X LR X X=, . <...> Besides, ()LR X Y, contains Banach space Ho ()m X Y, of linear bounded operators (homomorphisms), defined on X with values in Y. If XY =, then () ( LO X LO X X=, , and End X is <...>