Related papers: The multidimensional truncated Moment Problem: Ato…
An analysis is given as to why one can not directly evaluate continuum moment equations, i.e., equations involving powers of the position variable times charge, current, or energy/momentum operators, on the lattice. I examine two cases: a…
The paper treats several aspects of the truncated matricial $[\alpha,\beta]$-Hausdorff type moment problems. It is shown that each $[\alpha,\beta]$-Hausdorff moment sequence has a particular intrinsic structure. More precisely, each element…
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
Representation formulas for faces and support functions of the values of maximal monotone operators are established in two cases: either the operators are defined on uniformly Banach spaces with uniformly convex duals, or their domains have…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We characterize when the level sets of a continuous quasi-monotone functional defined on a suitable convex subset of a normed space can be uniquely represented by a family of bounded continuous functionals. Furthermore, we investigate how…
The nuclear magnetic moment is an important physical observable and serves as a useful tool for the stringent test of nuclear models. For the past decades, the covariant density functional theory and its extension have been proved to be…
We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
We consider $m$ integral vectors $X_1,...,X_m \in \mathbb{Z}^s$ located in a half-space of $\mathbb{R}^s$ ($m\ge s\geq 1$) and study the structure of the additive semi-group $X_1 \mathbb{N} +... + X_m \mathbb{N}$. We introduce and study…
The main result of the paper gives criteria for extendibility of sesquilinear form-valued mappings defined on symmetric subsets of *-semigroups to positive definite ones. By specifying this we obtain new solutions of: * the truncated…
The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem. The growth at…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of…
This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper we obtain a Nevanlinna-type formula for this moment problem…