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On the spectrum of periodic perturbations of certain unbounded Jacobi operators

Sahbani J.

Opuscula Mathematica

2016

Vol. 36, no. 6

807--818

It is known that a purely off-diagonal Jacobi operator with coefficients [formula] has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum.

Decisiveness of the spectral gaps of periodic Schrodinger operators on the Dumbbell-like metric graph

Niikuni H.

Opuscula Mathematica

2015

Vol. 35, no. 2

199--234

In this paper, we consider periodic Schrodinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.

Spectral gap estimate for stable processes on arbitrary bounded open sets

Kwaśnicki M.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

163--167

In the paper we prove the lower bound estimate λD2 −λDD1≥c(λD1)−d−α(diamD−d−α) for the spectral gap of the Dirichlet fractional Laplacian (−(−Δ)α/2) on an arbitrary bounded open set D⊂ Rd.