On the Bernstein inequality for rational functions with a prescribed zero
Abbreviated Journal Title
J. Approx. Theory
rational functions; Bernstein inequality; Blaschke product; POLYNOMIALS; Mathematics
We extend some results of Giroux and Rahman (Trans. Amer. Math. Soc. 193 (1974), 67-98) for Bernstein-type inequalities on the unit circle for polynomials with a prescribed zero at z=1 to those for rational functions. These results improve the Bernstein-type inequalities for rational functions. The sharpness of these inequalities is also established. Our approach makes use of the Malmquist-Walsh system of orthogonal rational functions on the unit circle associated with the Lebesgue measure. (C) 1998 Academic Press.
Journal of Approximation Theory
"On the Bernstein inequality for rational functions with a prescribed zero" (1998). Faculty Bibliography 1990s. 2296.