Coefficients of Polynomials of Restricted Growth on the Real Line Original Research Article

Letφ: (−∞, ∞)→(0, ∞) be a given continuous even function and letmbe a positive integer. We show that, with some additional restrictions onφ, there exist decreasing sequencesx1, …, xmandy1, …, ym−1of symmetrically located points on (−∞, ∞) and corresponding polynomialsPandQof degreesm−1 andm, respectively, satisfying|P(x)|⩽φ(x)m, |Q(x)|⩽φ(x)m, −∞