Abstract:
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 ∑kλkh(λkz) with parameters λk∈E, where E is a compact subset of ¯¯¯¯¯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).
This work was supported
by the Russian Foundation for Basic Research
under grant 18-01-00333 and
by the Presidential Program for the State Support of Leading Scientific Schools
under grant NSh-6222.2018.1.
\Bibitem{Bor18}
\by P.~A.~Borodin
\paper Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 1
\pages 3--10
\mathnet{http://mi.mathnet.ru/mzm11666}
\crossref{https://doi.org/10.4213/mzm11666}
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\transl
\jour Math. Notes
\yr 2018
\vol 104
\issue 1
\pages 3--9
\crossref{https://doi.org/10.1134/S0001434618070015}
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https://www.mathnet.ru/eng/mzm11666
https://doi.org/10.4213/mzm11666
https://www.mathnet.ru/eng/mzm/v104/i1/p3
This publication is cited in the following 3 articles:
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
M. A. Komarov, “On the rate of approximation in the unit disc of H1-functions by logarithmic derivatives of polynomials with zeros on the boundary”, Izv. Math., 84:3 (2020), 437–448
P. Chunaev, “Interpolation by generalized exponential sums with equal weights”, J. Approx. Theory, 254 (2020), UNSP 105397
Citation in format AMSBIB
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