Related papers: Compressive Identification of Linear Operators
We prove that for a homogeneous linear partial differential operator $\mathcal A$ of order $k \le 2$ and an integrable map $f$ taking values in the essential range of that operator, there exists a function $u$ of special bounded variation…
The localization spread gives a criterion to decide between metallic versus insulating behaviour of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different…
The problem of distributed identification of linear stochastic system with unknown coefficients over time-varying networks is considered. For estimating the unknown coefficients, each agent in the network can only access the input and the…
Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…
The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system. Verifying whether the parameters are identifiable is a necessary first…
The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed…
For entire operators and entire operators in the generalized sense, we provide characterizations based on the spectra of their selfadjoint extensions. In order to obtain these spectral characterizations, we discuss the representation of a…
This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any…
We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…
The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t…
In this study, we explore the partial identification of nonseparable models with continuous endogenous and binary instrumental variables. We show that the structural function is partially identified when it is monotone or concave in the…
This paper characterizes a new parametrization of nonlinear networked incrementally $L_2$-bounded operators in discrete time. The distinctive novelty is that our parametrization is \emph{free} -- that is, a sparse large-scale operator with…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
A bounded linear operator between Banach spaces is called {\it completely continuous} if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous…
This work focuses on the generic identifiability of dynamical networks with partial excitation and measurement: a set of nodes are interconnected by transfer functions according to a known topology, some nodes are excited, some are…
The Hilbert transform $H$ satisfies the Bedrosian identity $H(fg)=fHg$ whenever the supports of the Fourier transforms of $f,g\in L^2(R)$ are respectively contained in $A=[-a,b]$ and $B=R\setminus(-b,a)$, $0\le a,b\le+\infty$. Attracted by…
Over the past decades, the concept "partial smoothness" has been playing as a powerful tool in several fields involving nonsmooth analysis, such as nonsmooth optimization, inverse problems and operation research, etc. The essence of partial…
The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…
For a class of variational problems with linear differential operator, we obtain a convenient form of the deviation identity, i.e., the value of the distance between approximated solutions and the exact ones. We illustrate the result with…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…