Let V be an affine algebraic variety over R (or any other real closed field R). We ask when it is true that every positive semidefinite (psd) polynomial function on V is a sum of squares (sos). Weâ€¦ (More)

Given an affine algebraic variety V over R with compact set V (R) of real points, and a non-negative polynomial function f âˆˆ R[V ] with finitely many real zeros, we establish a local-global criterionâ€¦ (More)

Let g1, . . . , gr âˆˆ R[x1, . . . , xn] such that the set K = {g1 â‰¥ 0, . . . , gr â‰¥ 0} in Rn is compact. We study the problem of representing polynomials f with f |K â‰¥ 0 in the form f = s0 + s1g1 + Â·â€¦ (More)

Given a fixed family of polynomials h1, . . . , hr âˆˆ R[x1, . . . , xn], we study the problem of representing polynomials in the form f = s0 + s1h1 + Â· Â· Â· + srhr (*) with sums of squares si . Let Mâ€¦ (More)

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 theâ€¦ (More)

Continuing our recent work in [5] we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider suchâ€¦ (More)

Consider real polynomials g1, . . . , gr in n variables, and assume that the subset K = {g1 â‰¥ 0, . . . , gr â‰¥ 0} of Rn is compact. We show that a polynomial f has a representation

Let A be a semilocal ring. We compare the set of positive semidefinite (psd) elements of A and the set of sums of squares in A. For psd f âˆˆ A, whether f is a sum of squares or not depends only on theâ€¦ (More)

Given two positive definite forms f, g âˆˆ R[x 0 ,. .. , xn], we prove that f g N is a sum of squares of forms for all sufficiently large N â‰¥ 0. We generalize this result to projective R-varieties X asâ€¦ (More)