We consider the problem of stable recovery of sparse signals of the form from their spectral
measurements, known in a bandwidth with absolute error not exceeding. We consider the …

We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with
arbitrary" off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes …

We prove upper and lower bounds for the spectral condition number of rectangular
Vandermonde matrices with nodes on the complex unit circle. The nodes are “off the grid,” …

We study rectangular Vandermonde matrices V with N+ 1 rows and s irregularly spaced
nodes on the unit circle, in cases where some of the nodes are “clustered” together–the …

We prove lower bounds for the smallest singular value of rectangular, multivariate
Vandermonde matrices with nodes on the complex unit circle. The nodes are “off the grid” …

In this paper, we analyze the capacity of super-resolution (SR) of one-dimensional positive
sources. In particular, we consider a similar setting as in Batenkov et al.(2020, Inf. Inference …

We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with
arbitrary “off the grid” nodes (equivalently, a rectangular Vandermonde matrix with the nodes …

We start a systematic study of the topology, geometry and singularities of the Prony varieties
$ S_q (\mu) $, defined by the first $ q+ 1$ equations of the classical Prony system $$\sum …

This is a survey paper discussing one specific (and classical) system of algebraic equations-
the so called" Prony system". We provide a short overview of its unusually wide connections …

We provide an overview of some results on the" geometry of error amplification" in solving
Prony system, in situations where the nodes near-collide. It turns out to be governed by the" …