Add to ORKGPositive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn] are constructed to have the additional property that the members of any collection of forms whose squares sum to f must share a nontrivial complex root in Cn
AbstractThere is a positive semidefinite biquadratic form that cannot be expressed as the sum of squ...
Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the prope...
Let x denote the real n-tuple (x1,…,xn), (xx… ) the iterated n-tuple (x1,…,xn,x1,…xn…), A = (a i j) ...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
AbstractPositive definite forms f∈R[x1,…,xn] which are sums of squares of forms of R[x1,…,xn] are co...
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, .....
Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly...
Hilbert's 17th problem asks that whether every nonnegative polynomial can be a sum of squares of rat...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractLet R[X] be the real polynomial ring in n variables. Pólya’s Theorem says that if a homogene...
AbstractWe introduce the concept of the continuous Pythagoras number Pc(S) of a subset S of a commut...
We give a continuous representation of positive semidefinite (psd) n-ary quadratic forms over an ord...
AbstractIt has long been known that every positive semidefinite function of R(x, y) is the sum of fo...
In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (rea...
AbstractThere is a positive semidefinite biquadratic form that cannot be expressed as the sum of squ...
Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the prope...
Let x denote the real n-tuple (x1,…,xn), (xx… ) the iterated n-tuple (x1,…,xn,x1,…xn…), A = (a i j) ...
Positive definite forms f 2 R[x1, . . . , xn] which are sums of squares of forms of R[x1, . . . , xn...
AbstractPositive definite forms f∈R[x1,…,xn] which are sums of squares of forms of R[x1,…,xn] are co...
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, .....
Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly...
Hilbert's 17th problem asks that whether every nonnegative polynomial can be a sum of squares of rat...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractLet R[X] be the real polynomial ring in n variables. Pólya’s Theorem says that if a homogene...
AbstractWe introduce the concept of the continuous Pythagoras number Pc(S) of a subset S of a commut...
We give a continuous representation of positive semidefinite (psd) n-ary quadratic forms over an ord...
AbstractIt has long been known that every positive semidefinite function of R(x, y) is the sum of fo...
In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (rea...
AbstractThere is a positive semidefinite biquadratic form that cannot be expressed as the sum of squ...
Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the prope...
Let x denote the real n-tuple (x1,…,xn), (xx… ) the iterated n-tuple (x1,…,xn,x1,…xn…), A = (a i j) ...