Orthogonal Polynomials, L2-Spaces and Entire Functions.
Polynomially Positive Definite Sequences.
Problème diophantien des moments et modèle d'Ising
Problème diophantien des moments et modèle d'Ising
Quasi-definiteness of generalized Uvarov transforms of moment functionals.
Reconstruction of algebraic sets from dynamic moments
We discuss an exact reconstruction algorithm for time expanding semi-algebraic sets given by a single polynomial inequality. The theoretical motivation comes from the classical -problem of moments, while some possible applications to 2D fluid moving boundaries are sketched. The proofs rely on an adapted co-area theorem and a Hankel form minimization.
Remarks on a moment problem and a problem of perfection of power methods of limitation
Semi-groupes de moments.
Semiperfect countable C-separative C-finite semigroups.
Semiperfect semigroups are abelian involution semigroups on which every positive semidefinite function admits a disintegration as an integral of hermitian multiplicative functions. Famous early instances are the group on integers (Herglotz Theorem) and the semigroup of nonnegative integers (Hamburger's Theorem). In the present paper, semiperfect semigroups are characterized within a certain class of semigroups. The paper ends with a necessary condition for the semiperfectness of a finitely generated...
Smoothed projection methods for the moment problem.
Solving moment problems by dimensional extension.
Solving -dimensional complex moment problems.
Stieltjes moment problem in general Gelfand-Shilov spaces
The Stieltjes moment problem is studied in the framework of general Gelfand-Shilov spaces, subspaces of the space of rapidly decreasing smooth complex functions, which are defined by imposing suitable bounds on their elements in terms of a given sequence M. Necessary and sufficient conditions on M are stated for the problem to have a solution, sometimes coming with linear continuous right inverses of the moment map, sending a function to the sequence of its moments. On the way, some results on the...
Stieltjes perfect semigroups are perfect
An abelian -semigroup is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian -semigroup is perfect if for each there exist and such that ...
The K-moment problem for compact semi-algebraic sets.
The moment problem for non-compact semialgebraic sets.
The Moment Problem in the Space C... (S).
The Stieltjes moment problem in vector lattices.
The truncated matrix trigonometric moment problem with an open gap
This paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no. 6, 786-797, and Ukrainian Math. J., 2013, 64, no. 8, 1199- 1214. In this paper we shall study the truncated matrix trigonometric moment problem with an additional constraint posed on the matrix measure MT(δ), δ ∈ B(T), generated by the seeked function M(x): MT(∆) = 0, where ∆ is a given open subset of T (called a gap). We present necessary and sufficient...
Transfinite diameter on curves, Hankel determinants and the moment problem
We discuss problems on Hankel determinants and the classical moment problem related to and inspired by certain Vandermonde determinants for polynomial interpolation on (quadratic) algebraic curves in ℂ².