Polynomials in โ[๐ฉ,๐ช] that are sums of squares in โ(๐ฉ,๐ช)
David B. Leep, Colin Starr ยท Proceedings of the American Mathematical Society ยท 2001
A positive semidefinite polynomial f โ R [ x , y ] f \in \mathbb {R}[x,y] is said to be ฮฃ ( m , n ) \Sigma (m,n) if f f is a sum of m m squares in R ( x , y ) \mathbb {R}(x,y) , but no fewer, and f f is a sum of n n squares in R [ x , y ] \mathbb {R}[x,y] , but no fewer. If f f is not a sum of polynomial squares, then we set n = โ n=\infty . It is known that if m โค 2 m \leq 2 , then m = n m=n . The Motzkin polynomial is known to be ฮฃ ( 4 , โ ) \Sigma (4,\i