2019
Том 71
№ 11

All Issues

Bordulyak M. T.

Articles: 2
Article (Ukrainian)

Boundedness of the l-Index of Laguerre–Pólya Entire Functions

Bordulyak M. T., Sheremeta M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 91-99

We investigate conditions on zeros of an entire function f of the Laguerre–Pólya class under which f is a function of bounded l-index.

Article (Russian)

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

Bordulyak M. T., Sheremeta M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1166–1182

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 .