Abstract:
Under various constraints on a compact subset KK of the complex plane C and a subset E⊂C disjoint from K, the problem of density in the space AC(K) (the space of functions that are
continuous on a compact set K and analytic in its interior) of the set of simple partial fractions (logarithmic derivatives of polynomials) with poles in E is studied. The present investigation also involves examining some properties of additive subgroups of a Hilbert space.
Bibliography: 19 titles.
Keywords:
simple partial fractions, uniform approximation, restriction on the poles, additive subgroup.
This publication is cited in the following 11 articles:
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
P. A. Borodin, “Approximation by Simple Partial Fractions: Universal Sets of Poles”, Math. Notes, 111:1 (2022), 3–6
P. A. Borodin, K. S. Shklyaev, “Approximation by simple partial fractions in unbounded domains”, Sb. Math., 212:4 (2021), 449–474
V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Extremal and approximative properties of simple partial fractions”, Russian Math. (Iz. VUZ), 62:12 (2018), 6–41
P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. Math., 81:6 (2017), 1080–1094
P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles. II”, Sb. Math., 207:3 (2016), 331–341
A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
P. A. Borodin, O. N. Kosukhin, “Quantitative Expressions for the Connectedness of Sets in Rn”, Math. Notes, 98:5 (2015), 707–713
P. Chunaev, “Least deviation of logarithmic derivatives of algebraic polynomials from zero”, J. Approx. Theory, 185 (2014), 98–106
P. A. Borodin, “Density of a semigroup in a Banach space”, Izv. Math., 78:6 (2014), 1079–1104
A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
Citation in format AMSBIB
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