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Ukrainian Mathematical Journal

, Volume 55, Issue 9, pp 1514–1521 | Cite as

On Zeros of One Class of Functions Analytic in a Half-Plane

  • B. V. Vynnyts'kyi
  • V. L. Sharan
Article
  • 25 Downloads

Abstract

We describe sequences of zeros of functions f ≢ 0 analytic in the half-plane \({\mathbb{C}}_ + = \{ z:\operatorname{Re} z >0\}\) and satisfying the condition \((\exists {\tau}_1 \in (0;1))(\exists c_1 >0)(\forall z \in {\mathbb{C}}_ + ):|f(z)| \leqslant c_1 \exp ({\eta}^{\tau }_1 (c_1 |z|)),\) where η: [0; +∞) → (0; +∞) is an increasing function such that the function ln η(r) is convex with respect to ln r on [1; +∞).

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • B. V. Vynnyts'kyi
    • 1
  • V. L. Sharan
    • 1
  1. 1.Drohobych Pedagogic UniversityDrohobych

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