Podal subspaces on the unit polydisk

Tom 149 / 2002

Kunyu Guo Studia Mathematica 149 (2002), 109-120 MSC: 46J15, 46H25, 47B35, 47B38. DOI: 10.4064/sm149-2-2


Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space $H^2(D)$. To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points. By the methods developed in this note, we can assess when a unitary (resp. similarity) orbit contains a podal (resp. an s-podal) point, and hence provide examples of orbits without such points.


  • Kunyu GuoDepartment of Mathematics
    Fudan University
    Shanghai, 200433, People's Republic of China

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