Approximation by simple partial fractions with constraints on the poles

Under various constraints on a compact subset of the complex plane and a subset disjoint from , the problem of density in the space (the space of functions that are continuous on a compact set and analytic in its interior) of the set of simple partial fractions (logarithmic derivatives of polynomials) with poles in is studied. The present investigation also involves examining some properties of additive subgroups of a Hilbert space. Bibliography: 19 titles.