• Publications
  • Influence
Sums of squares of regular functions on real algebraic varieties
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). WeExpand
  • 111
  • 11
Sums of squares on real algebraic curves
Abstract.Given an affine algebraic variety V over ℝ with real points V(ℝ) compact and a non-negative polynomial function f∈ℝ[V] with finitely many real zeros, we establish a local-global criterionExpand
  • 81
  • 10
Real and Étale cohomology
Real spectrum and real etale site.- Glueing etale and real etale site.- Limit theorems, stalks, and other basic facts.- Some reminders on Weil restrictions.- Real spectrum of X and etale site of .-Expand
  • 79
  • 6
The moment problem for non-compact semialgebraic sets
Example 4: The assertion for n ≤ 2 is true. Also, for odd n ≥ 3, the assertion is true, since in this case the curve C has exactly one point at infinity, which is real. If n ≥ 4 is even (and C isExpand
  • 88
  • 5
Sums of squares on real algebraic surfaces
AbstractConsider real polynomials g1, . . . , gr in n variables, and assume that the subset K = {g1≥0, . . . , gr≥0} of ℝn is compact. We show that a polynomial f has a representation in which theExpand
  • 70
  • 5
An Algebraic Perspective on Multivariate Tight Wavelet Frames
Recent advances in real algebraic geometry and in the theory of polynomial optimization are applied to answer some open questions in the theory of multivariate tight wavelet frames whose generatorsExpand
  • 24
  • 4
An elementary proof of Hilbertʼs theorem on ternary quartics
Abstract In 1888, Hilbert proved that every nonnegative quartic form f = f ( x , y , z ) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and usedExpand
  • 12
  • 4
Positivity and sums of squares: A guide to recent results
This paper gives a survey, with detailed references to the literature, on recent developments in real algebra and geometry concerning the polarity between positivity and sums of squares. After aExpand
  • 102
  • 3
Distinguished representations of non-negative polynomials
Abstract Let g 1 , … , g r ∈ R [ x 1 , … , x n ] such that the set K = { g 1 ⩾ 0 , … , g r ⩾ 0 } in R n is compact. We study the problem of representing polynomials f with f | K ⩾ 0 in the form f = sExpand
  • 44
  • 3