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- W3068697810 abstract "We consider sequences $ {lbrace rho_j rbrace}_{0}^{infty} $ $ (rho_0 mathclose{=} 1, rho_j mathclose{geq} 1) $, $ {lbrace alpha_j rbrace}_{0}^{infty} $ $ (alpha_0 mathclose{=} 1, alpha_j mathclose{=} 1 mathclose{-} (1/rho_j )) $, $ {lbrace W_j (x) rbrace}_{0}^{infty} mathclose{in} W $, where
 $$ W mathclose{=} lbrace {lbrace W_j (x) rbrace}_{0}^{infty} / W_0 (x) mathclose{equiv} 1, W_j (x) mathclose{>} 0, {W}_{j}^{prime} (x) mathclose{leq} 0, W_j (x) mathclose{in} C^infty [0,a] rbrace, $$
 $ C^infty [0,a] $ is the class of functions of infinitely differentiable. For such sequences we introduce systems of operators $ {lbrace {A}_{a,n}^{ast} f rbrace}_{0}^{infty} $, $ {lbrace tilde{A}_{a,n}^{ast} f rbrace}_{0}^{infty} $ and functions $ {lbrace {U}_{a,n} (x) rbrace}_{0}^{infty} $, $ {lbrace {Phi}_{n} (x,t) rbrace}_{0}^{infty} $. For a certain class of functions a generalization of Taylor–Maclaurin type formulae was obtained. We also introduce the concept of $ langle rho_j,W_j rangle $ generalized completely monotone functions and establish a theorem on their representation." @default.
- W3068697810 created "2020-08-24" @default.
- W3068697810 creator A5024631566 @default.
- W3068697810 date "2020-04-15" @default.
- W3068697810 modified "2023-09-26" @default.
- W3068697810 title "ON THE $ langle rho_j,W_j rangle $ GENERALIZED COMPLETELY MONOTONE FUNCTIONS" @default.
- W3068697810 doi "https://doi.org/10.46991/pysu:a/2020.54.1.035" @default.
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