THE ZEROS OF FABER POLYNOMIALS FOR AN M-CUSPED HYPOCYCLOID

The Faber polynomials for a region of the complex plane are of interes t as a basis for polynomial approximation of analytic functions. In th is paper we determine the location, density, and asymptotic behavior o f the zeros of Faber polynomials associated with the closed region bou nded by the,m-cusped hypocycloid with parametric equation [GRAPHICS] F or m = 2, the Faber polynomials are simply the classical Chebyshev pol ynomials for the segment [-2,2]; thus our results can be viewed as a s tudy of the algebraic and asymptotic properties of generalized Chebysh ev polynomials. (C) 1994 Academic Press, Inc