Related papers: Dynamical Sampling for Shift-preserving Operators
In this paper, we consider the problem of recovery of a burst-like forcing term in an initial value problem (IVP) in the framework of dynamical sampling. We introduce an idea of using two particular classes of samplers that allow one to…
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $L^2(\mathfrak{S})$ where $\mathfrak{S}$ is a second countable LCA group. The subspaces where the operators act are…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…
In this paper, we study random sampling on reproducing kernel space $V$, which is a range of an idempotent integral operator. Under certain decay condition on the integral kernel, we show that any element in $V$ can be approximated by an…
Let $X=\{x_i:i\in\mathbb{Z}\}$, $\dots<x_{i-1}<x_i<x_{i+1}<\dots$, be a sampling set which is separated by a constant $\gamma>0$. Under certain conditions on $\phi$, it is proved that if there exists a positive integer $\nu$ such that…
We introduce the J map using the Zak transform associated with the Weyl transform on $L^{2}(\mathbb{R}^{2n})$. We obtain a decomposition for a twisted shift-invariant subspace of $L^{2}(\mathbb{R}^{2n})$ as a direct sum of mutually…
This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable…
We consider finitely generated shift-invariant spaces (SIS) with additional invariance in $L^2(\R^d)$. We prove that if the generators and their translates form a frame, then they must satisfy some stringent restrictions on their behavior…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of…
One challenge of motion generation using robot learning from demonstration techniques is that human demonstrations follow a distribution with multiple modes for one task query. Previous approaches fail to capture all modes or tend to…
Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and investigate frames of the form $\{\rho(\xi)…
Generating grasp poses is a crucial component for any robot object manipulation task. In this work, we formulate the problem of grasp generation as sampling a set of grasps using a variational autoencoder and assess and refine the sampled…
Stochastic generators are essential to produce synthetic realizations that preserve target statistical properties. We propose GenFormer, a stochastic generator for spatio-temporal multivariate stochastic processes. It is constructed using a…
This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection…