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Location of nontrivial Gleason parts on the topological boundary of the polydisc - Was it described anywhere else besides in Bekken's PhD Thesis?

My PhD advisor and me need the exact description of the location of the non-trivial Gleason parts on the topological boundary of the polydisc $\mathbb{D}^n$. It was described in Otto B. Bekken's PhD ...
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Decomposition of a contractive representation into an orthogonal sum for the $n$-dimensional case. Has this been done yet?

I know that it has been done for the two-dimensional case. Marek Kosiek showed it in his work "Decomposition of operator representations of the algebra $R(K_1 \times K_2)$" and "...
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