Abstract
We prove that, under certain conditions on a positive functionl continuous on [0, +∞], there exists an entire transcendental functionf of boundedl-index such that lnlnM f(r)lnL(r),r→∞, whereM f (r)=max {|f(z)|: |z|=r} andL(r)=∫ r0 l(t)dt. Ifl(r)=r p-1 forr≥1, 0<ρ<∞, then there exists an entire functionf of boundedl-index such thatM f (r)≈r p.
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Additional information
Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1166–1182, September, 1996.
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Bordulyak, M.T., Sheremeta, M.N. On the existence of entire functions of boundedl-index andl-regular growth. Ukr Math J 48, 1322–1340 (1996). https://doi.org/10.1007/BF02595355
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DOI: https://doi.org/10.1007/BF02595355