Abstract
It is shown that if a compact set not separating the plane lies in the union of the bounded components of the complement of another compact set , then the simple partial fractions (the logarithmic derivatives of polynomials) with poles in are dense in the space of functions that are continuous on and analytic in its interior. It is also shown that if a compact set with connected complement lies in the complement of the closure of a doubly connected domain with bounded connected components of the boundary and , then the differences of the simple partial fractions such that has its poles in and has its poles in are dense in the space . Bibliography: 9 titles.
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