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Full-Text Articles in Physical Sciences and Mathematics
The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko
The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko
Mathematics Faculty Publications
We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in …
On The Regularity Of The Critical Point Infinity Of Definitizable Operators, Branko Ćurgus
On The Regularity Of The Critical Point Infinity Of Definitizable Operators, Branko Ćurgus
Mathematics Faculty Publications
In this note necessary and sufficient conditions for the regularity of the critical point infinity of a definitizable operator A are given. Using these criteria it is proved that the regularity of the critical point infinity is preserved under some additive perturbations as well as for some operators which are related to A. Applications to indefinite Sturm-Liouville problems are indicated.