Podal subspaces on the unit polydisk

Kunyu Guo ¹

¹ Department of Mathematics Fudan University Shanghai, 200433, People's Republic of China

Studia Mathematica, Tome 149 (2002) no. 2, pp. 109-120

Résumé

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.

Détail

DOI : 10.4064/sm149-2-2

Keywords: beurlings classical theorem gives complete characterization invariant subspaces hardy space generalize theorem higher dimensions naturally led determining structure each unitary equivalence resp similarity class turn requires finding podal resp s podal points unitary resp similarity orbits note h outer resp g outer functions play important role finding podal resp s podal points methods developed note assess unitary resp similarity orbit contains podal resp s podal point hence provide examples orbits without points