Generalization of the fricke theorem on entire functions of finite index

• Date: 1996
• Main Authors: Sheremeta, M. M., Шеремета, М. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5338
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index....