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This matrix induces formally the operator $$\\mathcal{H}_\\mu (f)(z)= \\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty} \\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\mathbb D $. This is a natural generalization of the classical Hilbert operator. 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