The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of and then using the Stieltjes inversion formula.
In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.
Let V be a ℂ-space, be a pre-braid operator and let This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra . If and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...
We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in -norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated -norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated with systems...