ON APPROXIMATION BY BIVARIATE INCOMPLETE POLYNOMIALS

In this paper we prove that given certain convex domains DELTA on the plane, epsilon > 0, and f is-an-element-of C(DELTA) such that f = 0 on theta2DELTA = {(theta2x, theta2y): (x, y) is-an-element-of DELTA} (0 < theta < 1), a polynomial p(x, y) of the form [GRAPHICS] exists such that \\f - p\\C(DELTA) less-than-or-equal-to epsilon. The admissible convex domains include triangles and parallelograms with a vertex at the origin and sections of unit disk.