Related papers: Compressive Identification of Linear Operators
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state of the system is described by a probability measure and its evolution is given by the action of a nonlinear operator, also…
A network is called localizable if the positions of all the nodes of the network can be computed uniquely. If a network is localizable and embedded in plane with generic configuration, the positions of the nodes may be computed uniquely in…
We consider the problem of learning linear operators under squared loss between two infinite-dimensional Hilbert spaces in the online setting. We show that the class of linear operators with uniformly bounded $p$-Schatten norm is online…
A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…
A continuous linear operator L defined on the space of entire functions H(C) is said to be an extended $lambda$-eigenoperator of the differentiation operator D provided DL = $lambda$LD. Here we fully characterize when an extended…
We consider the design of functional estimators, i.e., approaches to compute an estimate of a nonlinear function of the state of a general nonlinear dynamical system subject to process noise based on noisy output measurements. To this end,…
Koopman operator, as a fully linear representation of nonlinear dynamical systems, if well-defined on a reproducing kernel Hilbert space (RKHS), can be efficiently learned from data. For stability analysis and control-related problems, it…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
We determine necessary and sufficient conditions on the ring of differential operators of a finite purely inseparable field extension of positive characteristic for determining whether the extension is modular.
We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark…
This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end…
This paper presents a general definition of pseudo-differential operators of type $1,1$; the definition is shown to be the largest one that is both compatible with negligible operators and stable under vanishing frequency modulation.…
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…
The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact…
For semi-Riemannian manifolds of constant sectional curvature, the Calabi operator is a second order linear differential operator that provides local integrability conditions for the range of the Killing operator. In this article, extending…
Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous…
Learning governing dynamics from data is a common goal across the sciences, yet it is only well-posed when the underlying mechanisms are identifiable. In practice, many data-driven methods implicitly assume identifiability; when this…
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…