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On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
Leonid Golinskii, Anton Kutsenko
We construct a functional model (direct integral expansion) and study the spectra of certain periodic block-operator Jacobi matrices, in particular, of general 2D partial differenc…
Algebra of 2D periodic operators with local and perpendicular defects
Anton A. Kutsenko
We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectr…
Application of matrix-valued integral continued fractions to spectral problems on periodic graphs
Anton A. Kutsenko
We show that spectral problems for periodic operators on lattices with embedded defects of lower dimensions can be solved with the help of matrix-valued integral continued fraction…
Nanoribbons in external electric fields
Evgeny Korotyaev, Anton Kutsenko
We consider the Schrödinger operator on nanoribbons (tight-binding models) in an external electric potentials . The corresponding electric field is perpendicular to the axis of…
Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients
Evgeny Korotyaev, Anton Kutsenko
We give a simple proof of Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients.
Lyapunov functions for periodic matrix-valued Jacobi operators
Evgeny Korotyaev, Anton Kutsenko
We consider periodic matrix-valued Jacobi operators. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov func…