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LeanPool.OperatorTheory.Operator.Crouzeix.DiskMergelyan

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.

Every complex function differentiable on an open disk and continuous on its closure is a compact-uniform limit of complex polynomials.