相关论文: Multivariable moment problems

Let $K_f$ be a closed semi-algebraic set in $\dR^d$ such that there exist bounded real polynomials $h_1,{...},h_n$ on $K_f$. It is proved that the moment problem for $K_f$ is solvable provided it is for all sets $K_f\cap C_\lambda$, where…

We study the universal C^*-algebras generated by n projections $p_1, >..., p_n$ subject to the relation $p_1+... p_n = \lambda 1$, $\lambda \in \mathbb R$. The questions of when these C^*-algebras are type I, nuclear or exact are…

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…

When the algebraic variety associated with a truncated moment sequence is finite, solving the moment problem follows a well-defined procedure. However, moment problems involving infinite algebraic varieties are more complex and less…

We design new deterministic and randomized algorithms for computational problems in free solvable groups. In particular, we prove that the word problem and the power problem can be solved in quasi-linear time and the conjugacy problem can…

The $k$-subset sum problem over finite fields is a classical NP-complete problem.Motivated by coding theory applications, a more complex problem is the higher $m$-th moment $k$-subset sum problem over finite fields. We show that there is a…

We extend Haviland's theorem on the integral representation of positive linear functionals on usual (real multivariate) polynomials to the integral representation of positive linear maps on operator polynomials mapping into the space of…

For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of…

We compute the K-theory of the C*-algebra of symmetric words in two universal unitaries. This algebra is the fixed point C*-algebra for the order-two automorphism of the full C*-algebra of the free group on two generators which switches the…

A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…

Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.

We investigate the generalized moment membership problem for matrices, a formulation equivalent to Skolem's problem for linear recurrence sequences. We show decidability for orthogonal, unitary, and real eigenvalue matrices, and…

The main purpose of this article is to explore the possibility of extending the notion of peripheral Poisson boundary of unital completely positive (UCP) maps to contractive completely positive (CCP) maps and to unital and non-unital…

Two Poisson structures invariant with respect to discrete transformation of the Maximal root in the case of arbitrary semi-simple algebras are presented in explicit form. Thus the problem of construction of equations of n-wave hierarchy in…

A class of Poisson embeddings of reduced, finite dimensional symplectic vector spaces into the dual space $\Lg_R^*$ of a loop algebra, with Lie Poisson structure determined by the classical split $R$--matrix $R=P_+ - P_-$ is introduced.…

We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible $G$-complex employing the theory of minimal classes of quadratic…

Let Phi : M --> g^* be a proper moment map associated to an action of a compact connected Lie group, G, on a connected symplectic manifold, (M,\omega). A collective function is a pullback via \Phi of a smooth function on g^*. In this paper…

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

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…