Related papers: Sampling The Lowest Eigenfunction to Recover the P…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the…
In this paper, we derive an asymptotic approximation to the eigenvalues of the linear differential equation $$ -y"(x)+q(x)y(x)=\lambda y(x), x\in (a,b) $$ with boundary conditions of general form, when $q$ is a measurable function which has…
In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering…
The paper suggests a method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy. The problem is considered in the pathwise…
In dimension 1, we show that the Taylor expansion of a potential near a generic non degenerate critical point can be recovered from the knowledge of the semi-classical spectrum of the associated Schr\"odinger operator near the corresponding…
We recover a nonlinear magnetic Schr\"odinger potential from measurement on an arbitrarily small open subset of the boundary on a compact Riemann surface. We assume that the magnetic potential satisfies suitable analytic properties, in…
We study formally determined inverse problems with passive measurements for one dimensional evolution equations where the goal is to simultaneously determine both the initial data as well as the variable coefficients in such an equation…
This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…
The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…
We analyze transition potentials $(V(r) \stackrel{r\sim 0}{\rightarrow} {\alpha r^{-2}})$ in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range $-1/4 < \alpha < 3/4$, the eigenvalue problem becomes…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
We continue the study of the A-amplitude associated to a half-line Schrodinger operator, -d^2/dx^2+ q in L^2 ((0,b)), b <= infinity. A is related to the Weyl-Titchmarsh m-function via m(-\kappa^2) =-\kappa - \int_0^a A(\alpha)…
A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small…
By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schr\"odinger operators with periodic singular potentials $v.$ Our results reveal a close relationship between smoothness of…
In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…
An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force…
The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding…
Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…