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Dirichlet series with positive real part
Published online by Cambridge University Press: 17 April 2009
Abstract
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We consider the sequence Λ = {0 < λ2 < λ2 < …}, for which λn → +∞. We denote by PD(Λ) the class of Dirichlet's series having the form F(s) = defined in the half plan Re s > 0 converging absolutely and Re F ≥ 0. If N0 = {0, 1,2, …} then the class PD(N0) coincides with the Caratheodory's class P. In this paper some classical results holding for the class P are generalised in any class PD(Λ). In special cases for the sequence Λ extreme problems are examined in the class PD(Λ).
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- Copyright © Australian Mathematical Society 1992
References
[1]Artemiadis, N., ‘Quelques resultat sur les transformees de Fourier avec applications’, Bull. Sc. Math. 97 (1973), 177–191.Google Scholar
[2]Holland, F., ‘The extreme points of a class of functions with positive real part’, Math. Ann. 202 (1973), 85–87.CrossRefGoogle Scholar
[3]Katznelson, Y., An introduction to harmonic analysis (John Wiley and Sons. Inc., New York, 1968).Google Scholar
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