Wandering vector multipliers for unitary groups Academic Article

abstract

• A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself. A special case of unitary system is a discrete unitary group. We prove that for many (and perhaps all) discrete unitary groups, the set of wandering vector multipliers is itself a group. We completely characterize the wandering vector multipliers for abelian and ICC unitary groups. Some characterizations of special wandering vector multipliers are obtained for other cases. In particular, there are simple characterizations for diagonal and permutation wandering vector multipliers. Similar results remain valid for irrational rotation unitary systems. We also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups. There are applications to wavelet systems. 2001 American Mathematical Society.

authors

• Larson, David

published proceedings

• Transactions of the American Mathematical Society

author list (cited authors)

• Han, D., & Larson, D.

complete list of authors

• Han, D||Larson, D

publication date

• December 2001

published in

• Transactions of the American Mathematical Society  Journal

start page

• 3347

end page

• 3370

volume

• 353

issue

• 8