Reducibility of positive type polynomials

Reducibility of Polynomials

Reducibility without qualification means in this lecture reducibility over the rational field. Questions on such reducibility occupy an intermediate place between questions on reducibility of polynomials over an algebraically closed field and those on primality. I shall refer to these two cases as to the algebraic and the arithmetic one and I shall try to exhibit some of the analogies consideri...

Reductibility of Positive Type Polynomials

A Question concerning Positive Type Polynomials

1. The problem. In [l], the following problem is posed: Let 0<A<1. Find the smallest integer re for which there exist re real numbers ai, a2, ■ ■ • , an such that the polynomial (y2 — 2Ay + T) ' II?-1 Cy+0») has all its coefficients non-negative. If N is such an integer, does there exist some real number a such that (y2 — 2Ay + l) •(y+a)N has only non-negative coefficients.1 In the process of g...

Semirecursive Sets and Positive Reducibility

positive lagrange polynomials

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...