Related papers: The $k$-adjacency operators and adjacency Jacobi m…
In this article we continue the study of the geometry of $k$-D'Atri spaces, $% 1\leq k$ $\leq n-1$ ($n$ denotes the dimension of the manifold)$,$ began by the second author. It is known that $k$-D'Atri spaces, $k\geq 1,$ are related to…
The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the $2M$-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new…
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…
The research on spectral inequalities for discrete Schrodinger Operators has proved fruitful in the last decade. Indeed, several authors analysed the operator's canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we…
The paper concerns with infinite symmetric block Jacobi matrices $\bf J$ with $p\times p$-matrix entries. We present new conditions for general block Jacobi matrices to be selfadjoint and have discrete spectrum. In our previous papers there…
The known correspondence between the Kronig-Penney model and certain Jacobi matrices is extended to a wide class of Schroedinger operators on graphs. Examples include rectangular lattices with and without a magnetic field, or comb-shaped…
Naturally reductive spaces, in general, can be seen as an adequate generalization of Riemannian symmetric spaces. Nevertheless, there are some that are closer to symmetric spaces than others. On the one hand, there is the series of Hopf…
The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…
In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…
The k-domination number of a graph is the minimum size of a set X such that every vertex of G is in distance at most k from X. We give a linear time constant-factor approximation algorithm for k-domination number in classes of graphs with…
We consider symmetric Jacobi operators with recurrence coefficients such that the corresponding difference equation is in the limit circle case. Equivalently, this means that the associated moment problem is indeterminate. Our main goal is…
We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there…
We provide a unified method to study the adjacency matrices of regular graphs (including infinite ones) using holomorphic functional calculus. By applying this calculus on a specific ellipse that contains the spectrum, we derive an…
We present a holomorphic representation of the Jacobi algebra $\mathfrak{h}_n\rtimes \mathfrak{sp}(n,\R)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}^n\times \mathcal{D}_n$. We construct…
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetric operators in a finite-dimensional Hilbert space we prove…
We extend the so-called Kotani Theory for a particular class of ergodic matrix-like Jacobi operators defined in $l^{2}(\mathbb{Z}; \mathbb{C}^{l})$ by the law $[H_{\omega} \textbf{u}]_{n} := D^{*}(T^{n - 1}\omega) \textbf{u}_{n - 1} +…
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…
In this notes unbounded regular operators on Hilbert $C^*$-modules over arbitrary $C^*$-algebras are discussed. A densely defined operator $t$ possesses an adjoint operator if the graph of $t$ is an orthogonal summand. Moreover, for a…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on…