2019
Том 71
№ 7

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On the existence of entire functions of bounded l-index and l-regular growth

Bordulyak M. T., Sheremeta M. M.

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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)=∫ 0 r 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 .

English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 9, pp 1322-1340.

Citation Example: Bordulyak M. T., Sheremeta M. M. On the existence of entire functions of bounded l-index and l-regular growth // Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1166–1182.

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