Asymptotics of the L² Norm of Derivatives of OPUC
Martinez-Finkelshtein, Andrei · Simon, Barry
Original · EN
We show that for many families of OPUC, one has ||φ'ₙ||₂/n -> 1, a condition we call normal behavior. We prove that this implies |αₙ| -> 0 and that it holds if the sequence αₙ is in ℓ¹. We also prove it is true for many sparse sequences. On the other hand, it is often destroyed by the insertion of a mass point.
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