Related papers: On the truncated two-dimensional moment problem
We have shown in a recent collaboration that the Cauchy problem for the multi-dimensional Burgers equation is well-posed when the initial data u(0) is taken in the Lebesgue space L 1 (R n), and more generally in L p (R n). We investigate…
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…
We present the new Guided Moments ($\texttt{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\texttt{M1}$) and Monte-Carlo…
We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each…
A theorem of Bayer and Teichmann implies that if a finite real multisequence \beta = \beta^(2d) has a representing measure, then the associated moment matrix M_d admits positive, recursively generated moment matrix extensions M_(d+1),…
We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
In this paper we study the problem -\Delta u =\left(\frac{2+\alpha}{2}\right)^2\abs{x}^{\alpha}f(\lambda,u), & \hbox{in}B_1 \\ u > 0, & \hbox{in}B_1 u = 0, & \hbox{on} \partial B_1 where $B_1$ is the unit ball of $\R^2$, $f$ is a smooth…
Given real numbers $\beta \equiv \beta ^{\left( 4\right) }\colon \beta_{00}$, $\beta _{10}$, $\beta _{01}$, $\beta _{20}$, $\beta _{11}$, $ \beta _{02}$, $\beta _{30}$, $\beta _{21}$, $\beta _{12}$, $\beta _{03}$, $\beta _{40}$, $\beta…
We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schr\"odinger equation $iu_t + \Delta u = \pm |u|^2 u$ for large spherically symmetric L^2_x(\R^2) initial data; in the focusing case we require,…
The $l_2$ flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction. It has been conjectured that the target dimension bounds can be refined and bounded in terms of the intrinsic dimensionality of the…
We prove the monotonicity of positive solutions to the problem $-\Delta u = f(u)$ in $\mathbb{R}^N_+ := \{(x',x_N)\in\mathbb{R}^N \mid x_N>0 \}$ under zero Dirichlet boundary condition with a possible singular nonlinearity $f$. In some…
Consider an $L^1$-continuous functional $\ell$ on the vector space of polynomials of Brownian motion at given times, suppose $\ell $ commutes with the quadratic variation in a natural sense, and consider a finite set of polynomials of…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
In this paper, we study the mass-constrained fractional Choquard equation \( (-\Delta)^s u = \lambda u + \alpha (I_\mu * |u|^{\frac{2N-\mu}{N}})|u|^{\frac{2N-\mu}{N}-2}u + (I_\mu * |u|^p)|u|^{p-2}u \) in \( \mathbb{R}^N \), under the…
The present paper is devoted to the {\it local moment problem}, which consists in finding of non-decreasing functions on the real axis having given first $2n+1, \; n\geq 0,$ power moments on the whole axis and also $2m+1$ first power…
Suppose that $a$ and $b$ are positive integers subject to $(a,b)=1$. For $n\in\mathbb{Z}^+$, denote by $\tau_{a,b}(n;\ell_1,M_1,l_2,M_2)$ the asymmetric two--dimensional divisor function with congruence conditions, i.e., \begin{equation*}…
In a 2014 paper, R.E. Curto and S. Yoo proved that a moment matrix $M(3)$ with specific harmonic polynomials as column relations admits a representing measure if and only if a condition at the level of moments holds. \ In this paper, we…
The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…