Spectral Synthesis for Operators and Systems

Inverse spectral problems for Sturm-Liouville operators with transmission conditions

Abstract: This paper deals with the boundary value problem involving the differential equation                      -y''+q(x)y=lambda y                                 subject to the standard boundary conditions along with the following discontinuity conditions at a point              y(a+0)=a1y(a-0),    y'(a+0)=a2y'(a-0)+a3y(a-0).  We develop the Hochestadt-Lieberman’s result for Sturm-Lio...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Linear functional equations, differential operators and spectral synthesis

We investigate the functional equation ∑n i=1 aif(bix + ciy) = 0, where ai, bi, ci ∈ C, and the unknown function f is defined on the field K = Q(b1, . . . , bn, c1, . . . , cn). (It is easy to see that every solution on K can be extended to C as a solution.) Let S1 denote the set of additive solutions defined on K. We prove that S1 is spanned by S1 ∩ D, where D is the set of the functions φ ◦ D...

Spectral decompositions for evolution operators of mixing dynamical systems

Spectral decompositions for the evolution operator on an energy shell in phase space are constructed for the free motion on compact 2D surfaces of constant negative curvature. Applications to quantum chaos and in particular to the recently proposed ballistic σ-model are briefly discussed.