On the Theory of the Spectrum of 2 х 2 Hyperbolic Systems of the Second Order

Abstract

The work is devoted to the investigation of the spectral characteristics of some boundary value problems for systems of linear differential equations in partial derivatives. The need to study the properties of the solvability of linear differential equation systems in partial derivatives occurs every time during the corresponding study of natural phenomena and processes. Important applications of the theory of systems of partial differential equations and problems associated with the study of the properties of the solvability of boundary value problems formulated to stimulate research relevant spectral problems. In the middle of the closed differential operator L :Ht ,x ®Ht ,x generated by the Dirichlet studied spectra: continuous C σ L and the residue R σ L spectra of closed operator L :Ht ,x ®Ht ,x form an empty set: CsL=RsL=AE . The point spectrum P σ L of operator L :Ht ,x ®Ht ,x is located on the real axis of the complex plane C . Own vector function of L-operator form a Riesz basis in the Hilbert space Ht,x.