Selfadjoint Sturm-Liouville operators Hω on L2(a, b) with random potentials are considered and it is proven, using positivity conditions, that for almost every ω the operator Hω does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as Hω but in L2(ã, b̃) where (ã, b̃) ⊂ (a, b).

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

The spectral flow is a well-known quantity in theory that measures the variation of spectra about 0 along paths selfadjoint Fredholm operators. aim this work twofold. Firstly, we consider homotopy invariance properties and establish simple formula which comprises its classical yields comparison theorem for under compact perturbations. We apply our result to existence non-trivial solutions bound...

We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action compact Lie group as an element representation ring latter. This G-equivariant shares all common properties integer valued classical flow, and it can be non-trivial even if vanishes. Our main theorem uses to study bifurcation periodic solutions autonomous Hamiltonian systems wi...

Our first aim is to clarify the results obtained by Lidskii devoted decomposition on root vector system of non-selfadjoint operator. We use a technique entire function theory and introduce so-called Schatten–von Neumann class convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms norm, we construct sequence contours power type that contr...

We consider the analytic continuation of the transfer function for a 2 × 2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis prope...