Open AccessOn uniform convergence of infinite products
Author(s) -
K. M. Slepenchuk,
G.A. Barbashova
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/247720
Subject(s) - convergence (economics) , mathematics , product (mathematics) , infinite product , class (philosophy) , uniform convergence , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , computer science , geometry , telecommunications , bandwidth (computing) , artificial intelligence , economics , economic growth
We establish necessary and sufficient conditions for $\{ \alpha_k(x) \}$ to satisfy such that the product $\prod\limits_{k=1}^{\infty} [1+\alpha_k(x) U_k(x)]$ converges uniformly under the condition that $\{ U_k(x) \}$ belongs to a given class.