Lower bounds for the merit factors of trigonometric polynomials from Littlewood classes Academic Article uri icon

abstract

  • With the notation K := ℝ (mod 2π), A formula is presented. We prove the following result. Theorem 1. Assume that p is a trigonometric polynomial of degree at most n with real coefficients that satisfies A formula is presented. Then M4(p) - M2 (p)≥EM2(p) with E := (1/111) (B/A)12. We also prove that M∞ (1 + 2p) - M2 (1 + 2p) ≥ ( 4/3-1) M2(1 + 2p) and M2(p) - M1 (p) ≥ 10-31 M2 (p) for every p ∈ An, where An denotes the collection of all trigonometric polynomials of the form p(t) := pn(t) :=∑ j=1 n aj cos (jt + αj), aj = ±1, αj ∈ ℝ. © 2003 Elsevier Inc. All rights reserved.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

citation count

  • 1

publication date

  • December 2003