Cyclicity in reproducing kernel Hilbert spaces of analytic functions

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We introduce a large family of reproducing kernel Hilbert spaces H ⊂ Hol(D), which include the classical Dirichlet-type spaces Dα, by requiring normalized monomials to form a Riesz basis for H. Then, after precisely evaluating the n-th optimal norm and the n-th approximant of f(z)=1-z, we completely characterize the cyclicity of functions in Hol(D) with respect to the forward shift.