An inequality for functions of exponential type not vanishing in a half-plane
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- by N. K. Govil PDF
- Proc. Amer. Math. Soc. 65 (1977), 225-229 Request permission
Abstract:
Let $f(z)$ be an entire function of order 1, type $\tau$ having no zero in $\operatorname {Im} \;z < 0$. If ${h_f}( - \pi /2) = \tau , {h_f}(\pi /2) \leqslant 0$ then it is known that ${\sup _{ - \infty < x < \infty }}|f’(x)| \geqslant (\tau /2){\sup _{ - \infty < x < \infty }}|f(x)|$. In this paper we consider the case when $f(z)$ has no zero in $\operatorname {Im} \;z < k, k \leqslant 0$ and obtain a sharp result.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 225-229
- MSC: Primary 30A64
- DOI: https://doi.org/10.1090/S0002-9939-1977-0454010-6
- MathSciNet review: 0454010