On the finiteness of the $l$-$\mathfrak{M}$-index of entire functions represented by series in а system of functions

• Date: 2024
• Main Authors: Sheremeta, M., Шеремета, Мирослав
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7866
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC517.5 Let $f$ be an entire transcendental function and let $(\lambda_n)$ be a sequence of positive numbers increasing to $+\infty.$ Suppose that the series $A(z)=\sum_{n=1}^{\infty}a_nf(\lambda_n z)$ is regularly convergent in ${\mathbb C},$ i.e., $\mathfrak{M}(r,A):=\sum_{n=1}^{\inf...