Abstract:A particular consequence of the famous Carleson-Hunt theorem is that the Taylor series expansions of bounded holomorphic functions on the open unit disk converge almost everywhere on the boundary, whereas on single points the convergence may fail. In contrast, there exists an ordinary Dirichlet series a n n −s , which on the open right half-plane [Re > 0] converges to a bounded, holomorphic function -but diverges at each point of the imaginary line, although its limit function extends continuously to the close… Show more
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