A remark on the multidimensional moment problem

  title={A remark on the multidimensional moment problem},
  author={Christian Berg and Jens Peter Reus Christensen and Christian U. Jensen},
  journal={Mathematische Annalen},
To mot ivate the following results let us recall some definitions and results with relation to the m o m e n t problem. Let (S, + ) be an abelian semigroup with neutral element 0. A real-valued function f : S ~ I R is called positive definite, if for any finite set of elements sl . . . . . s, s S the matr ix f(s~ + s) is positive semidefinite. The set ~ = ~ ( S ) of positive definite functions is easily seen to be a closed convex cone in the vector space i f (S) of all functions f : S--.IR with… 
Positivity, sums of squares and the multi-dimensional moment problem
Let K be the basic closed semi-algebraic set in R n defined by some finite set of polynomials S and T, the preordering generated by S. For K compact, f a polynomial in n variables nonnegative on K
The solvability of the Hausdorff moment problem for an arbi- trary compact subset of Euclidean n-space is shown to be equivalent to the nonnegativity of a family of quadratic forms derived from the
Moment problems in an infinite number of variables
Let ℝ∞ = × d=1∞ℝ. Given a closed set K ⊆ ℝ∞ and s : S∗→ ℝ, where S∗ denotes the set of tuples of nonnegative integers (n1,n2,…) with nd > 0 for finitely many d, the K-moment problem on ℝ∞ entails
Revisiting two theorems of Curto and Fialkow on moment matrices
We revisit two results of Curto and Fialkow on moment matrices. The first result asserts that every sequence y ∈ R Zn + whose moment matrix M(y) is positive semidefinite and has finite rank r is the
In Section 2 we prove a general result which gives sufficient conditions for the existence of a solution for a Markov-type moment problem in the space Lν(T ) (the implication (b)⇒ (a) of Theorem
On the Moment Problem and Related Problems
Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn  of real numbers and a closed
On the Relation between the Scalar Moment Problem and the Matrix Moment Problem on *-Semigroups
Abstract There is a countable cancellative commutative *-semigroup S withzero (in fact, a *-subsemigroup of G × N0 for some abelian group G carrying the inverse involution) such that the answer to
On Markov Moment Problem and Related Results
New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.


Topological Vector Spaces
This chapter presents the most basic results on topological vector spaces. With the exception of the last section, the scalar field over which vector spaces are defined can be an arbitrary,
On the Momentum Problem for Distribution Functions in More Than One Dimension. II
is likewise non-negative. A. Wintner has subsequently suggested that it should be possible to extend this result by requiring that the distribution function solving the problem have a spectrum
The problem of moments
This book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its
Über die Darstellung definiter Formen als Summe von Formenquadraten
Eine algebraische Form gerader Ordnung n mit reellen Koeffizienten und m homogenen Variablen moge definit heisen, wenn dieselbe fur jedes reelle Wertsystem der m Variablen einen positiven Wert
The Laplace Transform
(1945). What is the Laplace Transform? The American Mathematical Monthly: Vol. 52, No. 8, pp. 419-425.