Related papers: Dilatation operator and Cayley graphs

We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped…

In this article we study operators with a dimension $\Delta\sim O(N)$ and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are…

A derivative expansion technique is developed to compute functional determinants of quadratic operators, non diagonal in spacetime indices. This kind of operators arise in general 't Hooft gauge fixed Lagrangians. Elaborate applications of…

Starting from the classic definitions of local resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and spectrum, the local space and the single-valued extention property of a…

We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure.…

In this work, we focus on the multiplicity of singular spectrum for operators of the form $A^\omega=A+\sum_{n}\omega_n C_n$ on a separable Hilbert space $\mathcal{H}$, for a self-adjoint operator $A$ and a countable collection $\{C_n\}_{n}$…

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…

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of…

We introduce sufficient as well as necessary conditions for a compact set $K$ such that there is a continuous linear extension operator from the space of restrictions $C^\infty(K)=\lbrace F|_K: F\in C^\infty(\mathbb R)\rbrace$ to…

We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we…

Ordinary differential operators with periodic coefficients analytic in a strip act on a Hardy-Hilbert space of analytic functions with inner product defined by integration over a period on the boundary of the strip. Simple examples show…

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the…

We prove an analogue to the Cayley identity for an arbitrary self-adjoint operator in a Hilbert space. We also provide two new ways to characterize vectors belonging to the singular spectral subspace in terms of the analytic properties of…

This paper is a follow-up on the \emph{noncommutative differential geometry on infinitesimal spaces} [15]. In the present work, we extend the algebraic convergence from [15] to the geometric setting. On the one hand, we reformulate the…

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps $\g_n,n\ge 1$ with length $|\g_n|\ge 0$.…

A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturbation of a selfadjoint operator, and the spectral…

We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.

We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces…

We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term…

We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…