Approximation by simple partial fractions with constraints on the poles

P. A. Borodin

Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1553-1570

Résumé

Under various constraints on a compact subset $K$ of the complex plane $\mathbb C$ and a subset $E\subset \mathbb C$ 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.

Détail

Keywords: uniform approximation, restriction on the poles, additive subgroup.
Mots-clés : simple partial fractions

Bibliographie

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