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

• Datum: 1996
• Hauptverfasser: Bordulyak, M. T., Sheremeta, M. M., Бордуляк, М. Т., Шеремета, М. М.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1996
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/5232
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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