Related papers: Third order operator with small periodic coefficie…
We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two with $l\geq 6$, $l$ being an integer, and a limit-periodic potential $V(x)$. We prove that the spectrum contains a semiaxis of absolutely continuous spectrum.
In this paper we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential.
Spectral problem for a self-adjoint third-order differential operator with non-local potential on a finite interval is studied. Elementary functions that are analogues of sines and cosines for such operators are described. Direct and…
The spectrum of triangular band matrices defined on the sequence spaces where the entries of each band is a constant or convergent sequence is well studied. In this article, the spectrum and fine spectrum of a new generalised difference…
Using the symmetry properties of the three-anyon spectrum, we obtain exactly the multiplicities of states with given energy and angular momentum. The results are shown to be in agreement with the proper quantum mechanical and semiclassical…
We consider Schr\"odinger operators $H=-\Delta+V({\mathbf x})$ in ${\mathbb R}^d$, $d\geq2$, with quasi-periodic potentials $V({\mathbf x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis…
In this work it is described all normal extensions of a multipoint minimal operator generated by linear multipoint differential-operator expression for second order in the Hilbert space of vector-functions in terms of boundary values at the…
We study a class of pseudo-differential operators with oscillating symbols or osc illating amplitudes appearing in the long-range scattering theory. We develop the basic calc ulus for operators from such classes and solve some concrete…
This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems.…
We study Schr\"odinger operators on the real line whose potentials are generated by an underlying ergodic subshift over a finite alphabet and a rule that replaces symbols by compactly supported potential pieces. We first develop the…
This paper is devoted to the description of our recent results on the spectral behavior of one-dimensional adiabatic quasi-periodic Schrodinger operators. The specific operator we study is a slow periodic perturbation of an incommensurate…
We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by smoothness conditions, which preserve purely absolutely…
We present pretty detailed spectral analysis of Jacobi matrices with periodically modulated entries in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that the…
The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…
We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially supported by $[0,\infty)$ for almost every $t$.
Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…
We consider the Schr\"odinger operator on nanoribbons (tight-binding models) in an external electric potentials $V$. The corresponding electric field is perpendicular to the axis of the nanoribbon. If V=0, then the spectrum of the…
We consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. The spectrum of the Schr\"odinger operator consists of an absolutely continuous part (a union of a finite number of non-degenerated bands) plus a…
Spectrum of a first order sentence is the set of all $\alpha$ such that $G(n, n^{-\alpha})$ does not obey zero-one law w.r.t. this sentence. We have proved that the minimal number of quantifier alternations of a first order sentence with an…
We study the spectral multiplicity of Jacobi operators on star-like graphs with $m$ branches. Recently, it was established that the multiplicity of the singular continuous spectrum is at most $m$. Building on these developments and using…