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Reconstruction of algebraic sets from dynamic moments

Gabriela Putinar, Mihai Putinar (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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 L -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.

Semiperfect countable C-separative C-finite semigroups.

Torben Maack Bisgaard (2001)

Collectanea Mathematica

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...

Stieltjes moment problem in general Gelfand-Shilov spaces

Alberto Lastra, Javier Sanz (2009)

Studia Mathematica

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

Torben Maack Bisgaard, Nobuhisa Sakakibara (2005)

Czechoslovak Mathematical Journal

An abelian * -semigroup S is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on S 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 S is perfect if for each s ∈ S there exist t ∈ S and m , n ∈ ℕ 0 such that m + n ≥ 2 ...

The truncated matrix trigonometric moment problem with an open gap

Sergey Zagorodnyuk (2015)

Concrete Operators

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...

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