Uniform approximations by sums of bianalytic kernels, that is, sums of shifts of the function z/z are under consideration. Namely, we study conditions on a domain in the complex plane C and a set E C which ensure that each bianalytic function in can arbitrarily well be approximated locally uniformly in by sums of bianalytic kernels with singularities on E. Also, conditions on a compact set X are investigated ensuring that each continuous function on X that is bianalytic in the interior of X can arbitrarily well be approximated uniformly on X by sums of bianalytic kernels with singularities in C X. In both cases the necessary or sufficient conditions found are significantly different from the conditions in the corresponding results on approximations by simple partial fractions, that is, sums of shifts of the function 1/z. Bibliography: 19 titles.
Borodin et al. (Thu,) studied this question.