Related papers: On the Spectra of Real and Complex Lam\'e Operator…
Certain vertex operator algebras have integral forms (integral spans of bases which are closed under the countable set of products). It is unclear when they (or integral multiples of them) are integral as lattices under the natural bilinear…
Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…
We present general principles for the preservation of a.c. spectrum under weak perturbations. The Schrodinger operators on the strip and on the Caley tree (Bethe lattice) are considered.
In this paper, we first develop the theory of Musielak-Orlicz spaces on locally finite graphs, including completeness, reflexivity, separability, and so on. Then, we give some elementary properties of double phase operators on locally…
We introduce a family of post-critically finite fractal trees indexed by the number of branches they possess. Then we produce a Laplacian operator on graph approximations to these fractals and use spectral decimation to describe the…
We obtain $L^2$ decay estimates in $\lambda$ for oscillatory integral operators whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of…
As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on associative algebras and Lie algebras have played an important role in mathematics and physics.…
We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the…
We develop a Coulomb gas description of the critical fluctuations in the fully packed loop model on the honeycomb lattice. We identify the complete operator spectrum of this model in terms of electric and magnetic {\em vector}-charges, and…
We adapt the well-known spectral decimation technique for computing spectra of Laplacians on certain symmetric self-similar sets to the case of magnetic Schrodinger operators and work through this method completely for the diamond lattice…
By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schr\"odinger operators with periodic singular potentials $v.$ Our results reveal a close relationship between smoothness of…
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. An infinite series of trace formulae is obtained which link together two…
Results concerning set theoretic continuity properties of the spectrum of the Harper operator are extended to a large class (generalized Harper operators (GHO)) of operators in $L^{2}(\bZ^{2})$.
There are classical theorems of analysis which, given certain conditions on a perturbation, assert stability of the essential and absolutely continuous components of the spectrum of a self-adjoint operator. Whereas the singular component is…
We consider the unperturbed operator $H_0: = (-i \nabla - {\bf A})^2 + W$, self-adjoint in $L^2({\mathbb R}^2)$. Here ${\bf A}$ is a magnetic potential which generates a constant magnetic field $b>0$, and the edge potential $W = \bar{W}$ is…
We investigate the spectral topology of one-dimensional lattices where the nonreciprocal hoppings within the nearest $r_d$ neighboring sites are the same. For the purely off-diagonal model without onsite potentials, the energy spectrum of…
We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the…
In this paper, we introduce and study a new classes of operators, named AM-unbounded norm compact operators. We study the the basic properties of the new operator and we investigate the lattice-order and topology property of the operator…
Eigenvalues of the Lam\'e operator are studied as complex-analytic functions in period $\tau$ of an elliptic function. We investigate the branching of eigenvalues numerically and clarify the relationship between the branching of eigenvalues…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…