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The recovery of orthogonal polynomials from a sum of squares. (English) Zbl 0703.42019

Summary: It is shown that a positive polynomial of degree 2n has a unique representation as the sum of squares of polynomials of degrees 0 through n if the polynomials are real-valued and orthonormal with respect to some positive measure. The polynomials may be found by solving an electrostatic equilibrium problem.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
31A35 Connections of harmonic functions with differential equations in two dimensions
34A05 Explicit solutions, first integrals of ordinary differential equations
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