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

abstract

  • Sharp extensions of some classical polynomial inequalities of Bernstein are established for rational function spaces on the unit circle, on K = (mod 2), on [-1, 1] and on . 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) = nj = 1(z - aj) with |aj| 1 for each j, and for every z0D, where D = {zC: |z| = 1}. The above inequality is sharp at every z0D.

published proceedings

  • Mathematika

author list (cited authors)

  • Borwein, P., & Erdlyi, T.

citation count

  • 35

complete list of authors

  • Borwein, Peter||Erdélyi, Tamás

publication date

  • December 1996

publisher