APPROXIMATION BY POLYNOMIALS WITH RESTRICTED ZEROS

[摘要] This paper discusses convergence properties of polynomials whose zeros lie on the real axis or in the upper half-plane. A result of Levin shows that uniform convergence of such polynomials to a non-zero limit on a complex sequence converging not too East to a limit in the lower half-plane implies locally uniform convergence in C. We give a relatively simple proof of this result and present several extensions and examples which show that the criterion in Levin's theorem is almost sharp. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-01