On the Bernstein inequality for rational functions with a prescribed zero

    Authors

    R. Jones; X. Li; R. N. Mohapatra;R. S. Rodriguez

    Comments

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    Abbreviated Journal Title

    J. Approx. Theory

    Keywords

    rational functions; Bernstein inequality; Blaschke product; POLYNOMIALS; Mathematics

    Abstract

    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 Title

    Journal of Approximation Theory

    Volume

    95

    Issue/Number

    3

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    476

    Last Page

    496

    WOS Identifier

    WOS:000077443200005

    ISSN

    0021-9045

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