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On the Bernstein Inequality for Rational Functions with a Prescribed Zero

✍ Scribed by Roy Jones; Xin Li; R.N. Mohapatra; R.S. Rodriguez

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
390 KB
Volume
95
Category
Article
ISSN
0021-9045

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✦ Synopsis

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.

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## Abstract The main theme of this paper is the discussion of a parametrized family of solutions of a finite moment problem for rational matrix‐valued functions in the nondegenerate case. We will show that each member of this family is extremal in several directions concerning some point of the ope