Complex polynomial approximation on closed disks #
This file proves the disk model of the polynomial-approximation input used by the Crouzeix--Palencia smooth-exhaustion assembly. Boundary approximation is obtained by radially contracting into the open disk and taking a diagonal sequence of Taylor partial sums.
theorem
SmoothJordanDomain.ball_hasMergelyanPolynomialApproximation
(c : ℂ)
(R : ℝ)
(hR : 0 < R)
:
(ball c R hR).HasMergelyanPolynomialApproximation
Every complex function differentiable on an open disk and continuous on its closure is a compact-uniform limit of complex polynomials.