Geodesic
Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk
Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 3-10

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Given a function $h$ analytic in the unit disk $D$, we study the density in the space $A(D)$ of functions analytic inside $D$ of the set $S(h,E)$ of sums of the form $\sum_k\lambda_kh(\lambda_kz)$ with parameters $\lambda_k\in E$, where $E$ is a compact subset of $\overline D$. It is proved, in particular, that if the compact set $E$ “surrounds” the point $0$ and all Taylor coefficients of the function $h$ are nonzero, then $S(h,E)$ is dense in $A(D)$.
Keywords: approximation, analytic function, density, $h$-sum. 
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     author = {P. A. Borodin},
     title = {Approximation by {Sums} of the {Form} $\sum_k\lambda_kh(\lambda_kz)$ in the {Disk}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {104},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a0/}
}
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P. A. Borodin. Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk. Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a0/