On uniform convergence of infinite products

K.M. Slepenchuk (Dnipropetrovsk State University)
G.A. Barbashova (Dnipropetrovsk State University)

Abstract


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.

References


Slepenchuk K.M. "Nonlinear transformations of some classes of sequences (of products)", Izv. vuzov, 1964; 2. (in Russian)

Slepenchuk K.M. "Some indicators of convergence of infinite products", Izv. vuzov. Ser. Matem., 1971; 1. (in Russian)




DOI: https://doi.org/10.15421/247720

  

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Copyright (c) 1977 K.M. Slepenchuk, G.A. Barbashova

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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