Shibananda Biswas, Subrata Shyam Roy
Published 2013-01-14Version 1
In this note we characterize the distinguished boundary of the symmetrized polydisc and thereby develop a model theory for $\Gamma_n$-isometries along the lines of \cite{AY}. We further prove that for invariant subspaces of $\Gamma_n$-isometries, similar to the case $n=2$ \cite{S}, Beurling-Lax-Halmos type representation holds.
The invariant subspaces of $ S\oplus S^* $
Cyclic nearly invariant subspaces for semigroups of isometries
Invariant subspaces of $\mathcal{H}^2(\mathbb{T}^2)$ and $L^2(\mathbb{T}^2)$ preserving compatibility
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