Spectral analysis of singular ordinary differential operators with indefinite weights

On the Spectral Theory of Singular Indefinite Sturm-liouville Operators

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.

Recursive analysis of singular ordinary differential equations

We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elem...

Spectral properties of non - symmetric systems of ordinary differential operators

Spectral properties of singular Sturm-Liouville operators with indefinite weight sgnx

We consider a singular Sturm-Liouville expression with the indefinite weight sgnx. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in a neighbourhood of ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgnx)(−d2/dx2 + q) with non-real sp...

A Krein Space Approach to Symmetric Ordinary Differential Operators with an Indefinite Weight Function

l(f)=(-l)“(Pof’“‘)‘“‘+(-l)“-‘(p,f’”-”)’”~”+ ... +p,f=A.rf (0.1) on a finite or infinite interval (a, b) with real, locally summable coefficients l/PO,Pl, ..-3 Pnv r under the assumptions that p0 >O and that the weight function r changes its sign on (a, b). If r is positive, problem (0.1) can be studied in the context of Hermitian and self-adjoint operators in the Hilbert space L*(r) with the in...