# Claus Scheiderer

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- Publications
- Influence

Sums of squares of regular functions on real algebraic varieties

- Claus Scheiderer
- Mathematics
- 2000

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). We… Expand

Sums of squares on real algebraic curves

- Claus Scheiderer
- Mathematics
- 4 September 2003

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 criterion… Expand

Real and Étale cohomology

- Claus Scheiderer
- Mathematics
- 1994

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

The moment problem for non-compact semialgebraic sets

- V. Powers, Claus Scheiderer
- Mathematics
- 15 January 2001

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 is… Expand

Sums of squares on real algebraic surfaces

- Claus Scheiderer
- Mathematics
- 13 March 2006

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 the… Expand

An Algebraic Perspective on Multivariate Tight Wavelet Frames

- M. Charina, M. Putinar, Claus Scheiderer, J. Stöckler
- Mathematics
- 29 May 2013

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 generators… Expand

An elementary proof of Hilbertʼs theorem on ternary quartics

- A. Pfister, Claus Scheiderer
- Mathematics
- 16 September 2010

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 used… Expand

Positivity and sums of squares: A guide to recent results

- Claus Scheiderer
- Mathematics
- 2009

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 a… Expand

Distinguished representations of non-negative polynomials

- Claus Scheiderer
- Mathematics
- 15 July 2005

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 = s… Expand