Spurious limit functions of Taylor series (Q2318071)

Let \(\mathbb{D}\) be the unit open disc in \(\mathbb{C}\). Let \(H(\mathbb{D})\) be the space of all functions holomorphic in \(\mathbb{D}\). For a function \(f\in H(\mathbb{D})\) denote by \((S_n f)\) the sequence of partial sums of the Taylor series of \(f\) about \(0\). Let \(\mathbb{T}\) be the unit circle in \(\mathbb{C}\). The author investigates the convergence of the sequence \((S_n f)\) on \(\mathbb{T}\).