Related papers: Non-extremal sextic moment problems

Sufficient condition for the symmetric moment problem to be determinate is given using standards methods of $q$-Fourier analysis. This condition it cannot be a particular case of Carleman's criterion.

This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…

Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner…

In this paper, we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact…

This paper investigates the stochastic Ricker difference equation $X_{n+1} = X_n \exp(r(1-X_n)) \varepsilon_n$, where $X_n$ is a random variable representing the population size and $\{\varepsilon_n\}$ denotes independent random…

We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant…

The tensor rank decomposition problem consists of recovering the unique set of parameters representing a robustly identifiable low-rank tensor when the coordinate representation of the tensor is presented as input. A condition number for…

We study a semilinear elliptic equation with a pure power nonlinearity with exponent $p>1$, and provide sufficient conditions for the existence of positive solutions. These conditions involve expected exit times from the domain, $D$, where…

The two-dimensional moment problem consists of finding a positive Borel measure $\mu$ in $\mathbb{R}^2$ such that $\int_{\mathbb{R}^2} t_1^m t_2^n d\mu = s_{m,n}$, $m,n=0,1,2,...$, where $s_{m,n}$ are prescribed real constants (moments). We…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of…

This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

While any symmetric and positive semidefinite mapping can be the non-centered covariance of a Gaussian random field, it is known that these conditions are no longer sufficient when the random field is valued in a two-point set. The question…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

In this paper we study the strong matrix Stieltjes moment problem. We obtain necessary and sufficient conditions for its solvability. An analytic description of all solutions of the moment problem is derived. Necessary and sufficient…

We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…

By means of variational methods, in this paper, we establish sharp existence results for solutions of the master equations governing `fractional multiple vortices.' In the doubly periodic situation, the conditions for existence are both…

This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with…

Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertatinty relation, as well as a couple of…