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.
Beurling, On two problems concerning linear transformations in Hilbert space,Acta Math., 81: 239–255
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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.