Some inequalities for entire functions of exponential type
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- by Robert B. Gardner and N. K. Govil PDF
- Proc. Amer. Math. Soc. 123 (1995), 2757-2761 Request permission
Abstract:
If $f(z)$ is an asymmetric entire function of exponential type $\tau$, \[ \left \| f \right \| = \sup \limits _{ - \infty < x < \infty } |f(x)|,\] then according to a well-known result of R. P. Boas, \[ \left \| {f’} \right \| \leq \frac {\tau }{2}\left \| f \right \|\] and \[ |f(x + iy)| \leq \frac {{({e^{\tau |y|}} + 1)}}{2}\left \| f \right \|,\quad - \infty < x < \infty , - \infty < y \leq 0.\] Both of these inequalities are sharp. In this paper we generalize the above two inequalities of Boas by proving a sharp inequality which, besides giving as special cases the above two inequalities of Boas, yields some other results as well.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2757-2761
- MSC: Primary 30D15; Secondary 30A10
- DOI: https://doi.org/10.1090/S0002-9939-1995-1257107-7
- MathSciNet review: 1257107