A constructed holomorphic function in D_α* is cyclic for α < α* but not at α*, disproving persistence of cyclicity at the critical index via Riesz capacities of generalized Cantor sets.
Gautschi, Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function,Journal of Mathematics and Physics,38(1-4): 77–81
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Riesz $\alpha$-capacity of Cantor sets and cyclicity in Dirichlet-type spaces
A constructed holomorphic function in D_α* is cyclic for α < α* but not at α*, disproving persistence of cyclicity at the critical index via Riesz capacities of generalized Cantor sets.