Podal subspaces on the unit polydisk

Kunyu Guo. "Podal subspaces on the unit polydisk." Studia Mathematica 149.2 (2002): 109-120. <http://eudml.org/doc/284989>.

@article{KunyuGuo2002,
abstract = {Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(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.},
author = {Kunyu Guo},
journal = {Studia Mathematica},
keywords = {podal subspaces; Beurling theorem},
language = {eng},
number = {2},
pages = {109-120},
title = {Podal subspaces on the unit polydisk},
url = {http://eudml.org/doc/284989},
volume = {149},
year = {2002},
}

TY - JOUR
AU - Kunyu Guo
TI - Podal subspaces on the unit polydisk
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 2
SP - 109
EP - 120
AB - Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(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.
LA - eng
KW - podal subspaces; Beurling theorem
UR - http://eudml.org/doc/284989
ER -