Differential inequalities for entire functions of finite degree and rational functions with prescribed poles |
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Authors: | A V Olesov |
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Institution: | 1.Nevelskoy Maritime State University,Vladivostok,Russia |
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Abstract: | We establish new differential inequalities for the entire functions of finite degree with a majorant an entire function without
zeros in the lower half-plane, for the entire functions with constraints on zeros and, as a consequence, for the rational
functions with prescribed poles. All cases of equality in the main results are found. The estimates obtained generalize and
strengthen some inequalities by Bernstein, Gardner, and Govil for entire functions of finite degree; by Smirnov, Aziz, and
Shah for algebraic polynomials; and by Borwein and Erdelyi, Aziz and Shah, and the others for rational functions. |
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Keywords: | |
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