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Inequalities and representation formulas for functions of exponential type
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 58 / Issue 1 / February 1995
- Published online by Cambridge University Press:
- 09 April 2009, pp. 15-26
- Print publication:
- February 1995
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We generalise the classical Bernstein's inequality:
. Moreover we obtain a new representation formula for entire functions of exponential type.
. Moreover we obtain a new representation formula for entire functions of exponential type.Polynomials with a Prescribed Zero and the Bernstein's Inequality
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- Journal:
- Canadian Journal of Mathematics / Volume 45 / Issue 3 / 01 June 1993
- Published online by Cambridge University Press:
- 20 November 2018, pp. 627-637
- Print publication:
- 01 June 1993
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Let
be the class of all polynomials/? of degree at most n such that 
In view of the example zn it follows from Bernstein's inequality for polynomials that 
at each point z0 of the unitcirle. It was shown by A. Giroux and Q. I. Rahman [2] that if 
denotes the subclass of polynomials in which vanish at 1, then
where c1 and c2 are constants not depending on n. Here we find the exact value of
which has some special significance and also at certain other points of the unit circle.
be the class of all polynomials/? of degree at most n such that 
In view of the example 
at each point 
denotes the subclass of polynomials in 
which has some special significance and also at certain other points of the unit circle.