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cv.complicated variables – Two generalizations of the Verblunsky Theorem

I erudite from this paper about Verblunsky theorem.

My query is that: What kindly of generalizations of this theorem is availlable?

In specific I’m within the following two workable generalization:

1)Does each capricious sequence ${alpha_n} in mathbb{D}_4$ learn a exclusive chance touchstone on $S^3=partial mathbb{D}_4$?Does a queternion calculse ameliorate for such a generalization?

2)For which kindly of sequence ${alpha_n} in mathbb{C}^2simeq mathbb{C}P^2 setminus mathbb{C}P^1 $ we might secure a exclusive chance touchstone on $S^2=mathbb{C}P^1=partial mathbb{C}^2$?

To what extent the system of consideration of isometric group of the hyperbolic disck within the above paper breathe generalized in organize to respond to every of the above two questions?

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