Eigenfunction Expansions Associated With Singular Differential Operators

Eigenfunction Expansions for Schrödinger Operators on Metric Graphs

We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

Eigenfunction Expansions for Some Nonselfadjoint Operators and the Transport Equation*

There are many papers dealing with various aspects of the perturbation theory of a continuous spectrum [l-5, 12-151. In [3-51 some problems with nonselfadjoint operators were considered. In [3b] conditions for the perturbed operator to be similar to the unperturbed one are given. In [4] the Schrijdinger operator with a complex-valued potential was considered. In [S ] a theorem is announced in w...

On the Localization Eigenfunction Expansions Associated with the Schrodinger Operator

In this paper we study eigenfunction expansions associated with the Schrodinger operator with a singular potential. In the paper it is obtained sufficient conditions for localization and uniformly convergence of the regularizations of the corresponding expansions

Singular measure as principal eigenfunction of some nonlocal operators

In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution (λ, φ) of a nonlocal operator. ∫ Ω K(x, y)φ(y)dy + a(x)φ(x) = −λφ(x), where Ω ⊂ Rn is an open bounded connected set, K a nonnegative kernel and a is continuous. We prove that for the generalised principal ei...

Perturbation of eigenfunction expansions.