Relations of Borel Type for Generalizations of Exponential Series

• Datum: 2001
• Hauptverfasser: Skaskiv, O. B., Trusevich, О. M., Скасків, О. Б., Трусевич, О. М.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2001
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4379
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove that the condition \(\sum\nolimits_{n = 1}^{ + \infty } {\left( {n{\lambda }_n } \right)^{ - 1} < + \infty }\) is necessary and sufficient for the validity of the relation ln F(σ) ∼ ln μ(σ, F), σ → +∞, outside a certain set for every function from the class \(H_ + \left( {\lamb...