Add to ORKGHilbert's 17th problem asks that whether every nonnegative polynomial can be a sum of squares of rational functions. It has been answered affirmatively by Artin. However, the question as to whether a given nonnegative polynomial is a sum of squares of polynomials is still a central question in real algebraic geometry. In this paper, we solve this question completely for the nonnegative polynomials associated with isoparametric polynomials, initiated by E. Cartan, which define the focal submanifolds of the corresponding isoparametric hypersurfaces.Comment: 37pages, accepted by International Mathematics Research Notice
Abstract. Hilbert posed the following problem as the 17th in the list of 23 problems in his famous 1...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebrai...
The characteristic properties of Artin's denominators in Hilbert's 17th problem are obtained. It is ...
International audienceArtin solved Hilbert's 17th problem, proving that a real polynomial in $n$ var...
To prove that a polynomial is nonnegative on Rn, one can try to show that it is a sum of squares of ...
Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
In this paper we highlight the foundational principles of sums of squares in the study of Real Algeb...
Abstract. Hilbert posed the following problem as the 17th in the list of 23 problems in his famous 1...
AbstractCassels, Ellison, and Pfister have shown that there is a positive semidefinite function of R...
By a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x1, .....
63 pages ; publié au London Mathematical Society Journal of Computations and MathematicsInternationa...
Abstract. Hilbert posed the following problem as the 17th in the list of 23 problems in his famous 1...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebrai...
The characteristic properties of Artin's denominators in Hilbert's 17th problem are obtained. It is ...
International audienceArtin solved Hilbert's 17th problem, proving that a real polynomial in $n$ var...
To prove that a polynomial is nonnegative on Rn, one can try to show that it is a sum of squares of ...
Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
In this paper we highlight the foundational principles of sums of squares in the study of Real Algeb...
Abstract. Hilbert posed the following problem as the 17th in the list of 23 problems in his famous 1...
AbstractCassels, Ellison, and Pfister have shown that there is a positive semidefinite function of R...
By a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x1, .....
63 pages ; publié au London Mathematical Society Journal of Computations and MathematicsInternationa...
Abstract. Hilbert posed the following problem as the 17th in the list of 23 problems in his famous 1...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...