Spectral gaps of the periodic Schrödinger operator when its potential is an entire function

On spectral properties of Schrödinger–type operators with complex potential, Recent developments in operator theory and its applications, Operator Theory

We study deformations of the Plancherel measure of the symmetric group by lifting them to the symmetric group and using combina-torics of card shuffling. The existing methods for analyzing deformations of Plancherel measure are not obviously applicable to the examples in this paper. The main idea of this paper is to find and analyze a formula for the total variation distance between iterations ...

Schrödinger Operator on Homogeneous Metric Trees : Spectrum in Gaps

The paper studies the spectral properties of the Schrödinger operator A gV = A 0 + gV on a homogeneous rooted metric tree, with a decaying real-valued potential V and a coupling constant g ≥ 0. The spectrum of the free Laplacian A 0 = −∆ has a band-gap structure with a single eigenvalue of infinite multiplicity in the middle of each finite gap. The perturbation gV gives rise to extra eigenvalue...

Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps

Operator Theoretic Methods for the Eigenvalue Counting Function in Spectral Gaps

Using the notion of spectral flow, we suggest a simple approach to various asymptotic problems involving eigenvalues in the gaps of the essential spectrum of selfadjoint operators. Our approach uses some elements of the spectral shift function theory. Using this approach, we provide generalisations and streamlined proofs of two results in this area already existing in the literature. We also gi...

The Periodic Magnetic Schrödinger Operators: Spectral Gaps and Tunneling Effect

A periodic Schrödinger operator on a noncompact Riemannian manifold M such that H1(M, R) = 0 endowed with a properly discontinuous cocompact isometric action of a discrete group are considered. Under some additional conditions on the magnetic field existence of an arbitrary large number of gaps in the spectrum of such an operator in the semiclassical limit is established. The proofs are based o...