Extremal problems for certain analytic (Nevanlinna) functions |
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| Authors: | Maxwell O Reade Pavel G Todorov |
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| Institution: | 1. Department of Mathematics, University of Michigan, 48109, Ann Arbor, Michigan, U.S.A.
2. Department of Mathematics, Paissii Hilendarski University, 4000, Plovdiv, Bulgaria
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| Abstract: | We obtain sharp bounds on some basic functionals defined on the sets of all analytic functions having the representations \(f\left( z \right) \equiv \int\limits_{ - 1}^1 {\frac{{d\mu \left( t \right)}}{{z - t}}} \) and \(\varphi \left( z \right) \equiv \int\limits_{ - 1}^1 {\frac{{z\mu \left( t \right)}}{{1 - tz}}} \) ; respectively. Here μ is a probability measure. |
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