

Seminar on Complex Analysis (Gonchar Seminar)
February 9, 2015 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)






Approximations by simple partial fractions with constraints on the poles
P. A. Borodin^{} ^{} M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
We discusss the following new result: if the plane compact set $K$ has connected complement and is covered by the union $\widehat{E}\setminus E$ of bounded components of complement of another compact set $E$, then the simple partial fractions (logarithmic derivatives of polynomials) having all poles on $E$ are dense in the space $AC(K)$ of functions that are continuous on $K$ and analytic on its interior.

