On conditions for convergence of Taylor-Dirichlet series in a convex domain

• Date: 1994
• Main Authors: Krutigolova, Ye. K., Mel'nik, Yu. I., Крутиголова, Е. К., Мельник, Ю. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1994
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5599
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish necessary and sufficient conditions for the absolute convergence of the series $$\mathop \sum \limits_{v = 1}^\infty \sum\limits_{k = 0}^{m_v - I} {a_{v,k} z^k \exp (\lambda _v z)} $$ in an open region. We also give conditions under which an arbitrary function analytic in a closed re...