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Dive into the research topics where Salma Kuhlmann is active.

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Featured researches published by Salma Kuhlmann.


Transactions of the American Mathematical Society | 2002

Positivity, sums of squares and the multi-dimensional moment problem

Salma Kuhlmann; Murray Marshall

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 and real e > 0, we have that f + ∈ E T. In particular, the K-Moment Problem has a positive solution. In the present paper, we study the problem when K is not compact. For n = 1, we show that the K-Moment Problem has a positive solution if and only if S is the natural description of K (see Section 1). For n > 2, we show that the K-Moment Problem fails if K contains a cone of dimension 2. On the other hand, we show that if K is a cylinder with compact base, then the following property holds: (+) ∀ f ∈ R[X], f ≥ 0 on K ⇒ ∃q ∈ T such that ∀ real ∈ > 0, f + eq ∈ T. This property is strictly weaker than the one given in Schmudgen (1991), but in turn it implies a positive solution to the K-Moment Problem. Using results of Marshall (2001), we provide many (noncompact) examples in hypersurfaces for which () holds. Finally, we provide a list of 8 open problems.


arXiv: Commutative Algebra | 1997

Exponentiation in power series fields

Franz-Viktor Kuhlmann; Salma Kuhlmann; Saharon Shelah

We prove that for no nontrivial ordered abelian group G, the ordered power series fleld R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a non- surjective logarithm. For an arbitrary ordered fleld k, no exponen- tial on k((G)) is compatible, that is, induces an exponential on k through the residue map. This is proved by showing that certain functional equations for lexicographic powers of ordered sets are not solvable.


Transactions of the American Mathematical Society | 2008

Sums of squares and moment problems in equivariant situations

Jaka Cimpric; Salma Kuhlmann; Claus Scheiderer

We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group G over R acting on an affine R-variety V, we consider the induced dual action on the coordinate ring R[V] and on the linear dual space of R[V]. In this setting, given an invariant closed semialgebraic subset K of V(R), we study the problem of representation of invariant nonnegative polynomials on K by invariant sums of squares, and the closely related problem of representation of invariant linear functionals on R[V] by invariant measures supported on K. To this end, we analyse the relation between quadratic modules of R[V] and associated quadratic modules of the (finitely generated) subring R[V[ G of invariant polynomials. We apply our results to investigate the finite solvability of an equivariant version of the multidimensional K-moment problem. Most of our results are specific to the case where the group G(R) is compact.


Journal of Pure and Applied Algebra | 2002

Embedding ordered fields in formal power series fields

Franz-Viktor Kuhlmann; Salma Kuhlmann; Murray Marshall; M. Zekavat

In the paper it is shown how an embedding of an ordered field F into a formal power series field can be extended canonically to an embedding of any simple extension F(y) of F. Properties of the extended embedding are studied in detail. Several applications are given.


Proceedings of the American Mathematical Society | 1995

Isomorphisms of lexicographic powers of the reals

Salma Kuhlmann

Given a chain F, we consider the lexicographic order llr. If A is a chain such that Rr IRA, we examine the question of whether necessarily F A. Under an additional hypothesis, we show that F and A will have the same order types of well ordered subsets. Among other things, this yields an affirmative answer to the above question in the case where F and A are ordinals.


Archiv der Mathematik | 2013

The moment problem for continuous positive semidefinite linear functionals

Mehdi Ghasemi; Salma Kuhlmann; Ebrahim Samei

Let τ be a locally convex topology on the countable dimensional polynomial


Journal of Functional Analysis | 2014

Application of Jacobiʼs representation theorem to locally multiplicatively convex topological R-algebras

Mehdi Ghasemi; Salma Kuhlmann; Murray Marshall


Forum Mathematicum | 1996

Valuation Bases for Extensions of Valued Vector Spaces

Salma Kuhlmann

{\mathbb{R}}


Order | 1994

On ηα-groups and fields

Norman L. Alling; Salma Kuhlmann


Journal of Algebra | 2011

Hardy type derivations on fields of exponential logarithmic series

Salma Kuhlmann; Mickaël Matusinski

-algebra

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Murray Marshall

University of Saskatchewan

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Mehdi Ghasemi

University of Saskatchewan

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Paola D'Aquino

Seconda Università degli Studi di Napoli

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Saharon Shelah

Hebrew University of Jerusalem

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Charu Goel

University of Konstanz

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Claus Scheiderer

University of Erlangen-Nuremberg

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