THE FABER POLYNOMIALS FOR M-FOLD SYMMETRICAL DOMAINS

[摘要] The Faber polynomials for a region of the complex plane are of interest as a basis for polynomial approximations to analytic functions. In this paper we study the Faber polynomials associated with m-fold symmetric domains. Explicit formulae of Faber polynomials both for symmetric and nonsymmetric lemniscates are derived. In addition, we use a new determinant representation which relates the zeros of Faber polynomials to the eigenvalues of a certain matrix to compute the zeros of Faber polynomials for lemniscates.

[发布日期] 1994-10-20

[关键词] FABER POLYNOMIALS;M-FOLD SYMMETRICAL DOMAIN;M-LEAF LEMNISCATES