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Bernstein‐Type Inequalities for Rational Functions with Prescribed Poles
Author(s) -
Li Xin,
Mohapatra R. N.,
Rodriguez R. S.
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.3.523
Subject(s) - mathematics , unit circle , complex plane , inequality , rational function , norm (philosophy) , type (biology) , pure mathematics , polynomial , chebyshev filter , chebyshev polynomials , bernstein polynomial , mathematical analysis , algebra over a field , ecology , political science , law , biology
We establish Bernstein‐type inequalities for rational functions with prescribed poles in the Chebyshev norm on the unit circle in the complex plane. Generalizations of polynomial inequalities of Erdős‐Lax and Turán are also obtained for such rational functions with restricted zeros.