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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Haar integral of rational function of unitaries

I'm trying to compute the following Haar integral over the unitary group: $$ \int\limits_{\mathbb{U}(d)}\dfrac{1}{\sum_{k,l=1}^d u_{ik}\overline{u_{il}}c_{kl}}dU. $$ Is there anything known about the …