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The K Moment Problem has a positive solution y f R X f on K real f T In the present paper we consider the status of and y when K is not compact At the same time we consider a third property z f R X f on K q T such that real f q T which we prove is strictly weaker than y and at the same time which implies Many non compact examples are given where z holds… (More)

The paper is a continuation of work initiated by the first two authors in [K–M]. Section 1 is introductory. In Section 2 we give new proofs of results of Scheiderer in [S1] [S2] in the compact case; see Corollaries 2.3, 2.4 and 2.5. The main tool in Section 2, Lemma 2.1, is also used in Section 3 where we continue the examination of the case n = 1 initiated… (More)

- Murray Marshall
- 2006

Natural sufficient conditions for a polynomial to have a local minimum at a point are considered. These conditions tend to hold with probability 1. It is shown that polynomials satisfying these conditions at each minimum point have nice presentations in terms of sums of squares. Applications are given to optimization on a compact set and also to global… (More)

- Mehdi Ghasemi, Murray Marshall
- SIAM Journal on Optimization
- 2012

We make use of a result of Hurwitz and Reznick [8] [19], and a consequence of this result due to Fidalgo and Kovacec [5], to determine a new sufficient condition for a polynomial f ∈ R[X1, . . . , Xn] of even degree to be a sum of squares. This result generalizes a result of Lasserre in [10] and a result of Fidalgo and Kovacec in [5], and it also… (More)

- Murray Marshall
- 2000

The object of the paper is to extend part of the theory of-orderings on a skewweld with involution to a general ring with involution. The valuation associated to a-ordering is examined. Every-ordering is shown to extend.-orderings are shown to form a space of signs as deened by Brr ocker and Marshall. In case the involution is the identity, the ring under… (More)

- Murray Marshall
- 2004

real spectra [7, Chs. 6–8], also called spaces of signs [1, Ch. 3], arise naturally in the study of semialgebraic sets, more generally, in the study of constructible sets in the real spectrum of a commutative ring with 1. Let A denote the ring of all polynomial functions on V , where V ⊆ R is an algebraic set. Consider f, g ∈ A to be equivalent if f and g… (More)

- Murray Marshall
- 2008

We prove that if f(x, y) is a polynomial with real coefficients which is non-negative on the strip [0, 1] × R, then f(x, y) has a presentation of the form

- Murray Marshall
- 2010

We look for algebraic certificates of positivity for functions which are not necessarily polynomial functions. Similar questions were examined earlier by Lasserre and Putinar and by Putinar in [8, Proposition 1] and [14, Theorem 2.1]. We explain how these results can be understood as results on hidden positivity: The required positivity of the functions… (More)

- Murray Marshall
- 2003

Considerable work has been done in developing the relationship between ∗-orderings, ∗valuations and the reduced theory of Hermitian forms over a skewfield with involution [12] [13] [14] [15] [16] [23] [24]. This generalizes the well-known theory in the commutative case; e.g., see [4] [6] [7] [27]. In the commutative theory, formally real function fields… (More)

- Murray Marshall
- 2012

It is explained how the localization technique introduced by the author in [19] leads to a useful reformulation of the multivariate moment problem in terms of extension of positive semidefinite linear functionals to positive semidefinite linear functionals on the localization of R[x] at p = ∏n i=1(1 + x 2 i ) or p ′ = ∏n−1 i=1 (1 + x 2 i ). It is explained… (More)