Related papers: A note on discrete dynamical systems in theories o…
In this paper we study a connection between finite-gap on one energy level two-dimensional Schrodinger operators and two-dimensional discrete operators. We find spectral data for a new class of two-dimensional integrable discrete operators.…
An observability problem for linear autonomous distributed systems in the class of linear operations is considered. A criterion of observability with respect to terminal state has been proved. A connection with observability with respect to…
We study the global forms of class $\mathcal{S}[A_{N-1}]$ 4d $\mathcal{N} = 2$ theories by deriving their defect groups (charges of line operators up to screening by local operators) from Coulomb branch data. Specifically, we employ an…
We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
This paper gives combinatorial formulas for discrete series constants, both stable and unstable, on real reductive groups. It also carries out one step of the comparison of the topological trace formula for Hecke operators with Arthur's…
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…
We consider a class of line operators in d=4, N=2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call "framed BPS states." These include halo bound…
We study the BPS spectrum of four dimensional N=2 SU(2) theory with massive fundamental matters using the D3-brane probe. Since the BPS states are realized by string webs subject to the BPS conditions, we determine explicitly the…
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
We present and exploit an analogy between lack of absolutely continuous spectrum for Schroedinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke's example and natural boundary examples…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to a \textit{scalar product}, which we used to define \textit{orthogonals} in these…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
We classify self-adjoint first-order differential operators on weighted Bergman spaces on the $N$-dimensional unit ball $\mathbb{B}^N$ and $\mathbb{D}^2$ of $2\times2$ complex matrices satisfying $I-ZZ^*>0$.Our main tools are the discrete…
We characterize the spectrum (and its parts) of operators which can be represented as G=A+BC for a simpler operator A and a structured perturbation BC. The interest in this kind of perturbations is motivated, e.g., by perturbations of the…
An analytical-numerical analysis of the singular self-adjoint spectral problem for a system of three linear ordinary second-order differential equations defined on the entire real exis is presented. This problem comes to existence in the…
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…