• Corpus ID: 251066581

Approximate Pythagoras Numbers on $*$-algebras over $\mathbb{C}$

  title={Approximate Pythagoras Numbers on \$*\$-algebras over \$\mathbb\{C\}\$},
  author={Paria Abbasi and Sander Gribling and Andreas Klingler and Tim Netzer},
. The Pythagoras number of a sum of squares is the shortest length among its sums of squares representations. In many algebras, for example real polynomial algebras in two or more variables, there exists no upper bound on the Pythagoras number for all sums of squares. In this paper, we study how Pythagoras numbers in ∗ -algebras over C behave with respect to small perturbations of elements. More pre-cisely, the approximate Pythagoras number of an element is the smallest Pythagoras number among… 

Figures from this paper



Sum of squares length of real forms

For $$n,\,d\ge 1$$n,d≥1 let p(n, 2d) denote the smallest number p such that every sum of squares of degree d forms in $${\mathbb {R}}[x_1,\ldots ,x_n]$$R[x1,…,xn] is a sum of p squares. We establish

Zur Darstellung definiter Funktionen als Summe von Quadraten

Das Problem, definite Funktionen als Summe von Quadraten darzustellen, geht zuriick auf HILaERT. Er zeigte zuerst [4], dab fiir n > 2 ein positiv definites Polynom nicht notwendig Summe von

A course in convexity

  • A. Barvinok
  • Mathematics
    Graduate studies in mathematics
  • 2002
Convex sets at large Faces and extreme points Convex sets in topological vector spaces Polarity, duality and linear programming Convex bodies and ellipsoids Faces of polytopes Lattices and convex

Sum of Squares: Theory and Applications

  • Mathematics
    Proceedings of Symposia in Applied Mathematics
  • 2020

Sums of squares of real polynomials

The Pythagoras number of some affine algebras and local algebras.

For a (commutative) ring A, thepythagoras number, P(A), ofA is the smallest number n^oo such that any sum of squares in A can be expressed äs a sum of at most n squares in A. For instance, P(f?) = l,

A course in convexity, volume

  • Graduate Studies in Mathematics. Amer. Math. Soc.,
  • 2002

A course in convexity , volume 54 of Graduate Studies in Mathematics

  • 2002