Related papers: On the Band Functions and Bloch Functions
The article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which…
In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…
We discuss a functional model for multi--diagonal selfadjoint operators with almost periodic coefficients that generalizes the well known model for finite band Jacobi matrices. It give us an opportunity to construct examples of almost…
In this paper we investigate the spectrum of the differential operators generated by the ordinary differential expression of odd order with PT-symmertic periodic matrix coefficients
In this paper we consider the spectrum of the self-adjoint differential operator L generated by the differential expression of order n with the m by m periodic matrix coefficients, where n and m are respectively odd and even integers and…
We provide variational estimates for Bloch functions on the unit ball of $\mathbb{R}^d$ extending previous work on the Anderson conjecture for conformal maps on the unit disc.
Starting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an applications we find…
Every analytic self-map of the unit ball of a Hilbert space induces a bounded composition operator on the space of Bloch functions. Necessary and sufficient conditions for compactness of such composition operators are provided, as well as…
This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…
In this paper we characterize essential norm of composition operators on the spaces of Harmonic Bloch functions. These results extends the similar results that were proven for composition operators on Bloch spaces.
In this paper we obtain the asymptotic formulas of arbitrary order for the Bloch eigenvalues and Bloch functions of the multidimensional polyharmonic operator with periodic, with respect to arbitrary lattice, potential. Then we prove that…
In this paper we constructively determine a family of the spectral invariants of the multidimensional Schrodinger operator with a periodic potential by the given band functions.
Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences…
We consider the class of bounded self-adjoint Hankel operators $\mathbf H$, realised as integral operators on the positive semi-axis, that commute with dilations by a fixed factor. By analogy with the spectral theory of periodic…
We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the…
The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions…
In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of…
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite…
We give continued fraction expansions of the generating functions of Bernoulli numbers, Cauchy numbers, Euler numbers, harmonic numbers, and their generalized or related numbers. In particular, we focus on explicit forms of the convergents…