Sharp extensions of Bernstein's inequality to rational spaces Academic Article uri icon

abstract

  • Sharp extensions of some classical polynomial inequalities of Bernstein are established for rational function spaces on the unit circle, on K = ℝ (mod 2π), on [-1, 1] and on ℝ. The key result is the establishment of the inequality formula presented for every rational function f = pn/qn, where pnis a polynomial of degree at most n with complex coefficients and qn(z) = Πnj = 1(z - aj) with |aj| ≠ 1 for each j, and for every z0∈∂D, where ∂D = {z∈ℂC: |z| = 1}. The above inequality is sharp at every z0∈∂D.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

citation count

  • 27

publication date

  • December 1996