Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Wandering vector multipliers for unitary groups
HTML articles powered by AMS MathViewer

by Deguang Han and D. Larson PDF
Trans. Amer. Math. Soc. 353 (2001), 3347-3370 Request permission

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.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46L10, 46L51, 42C40
  • Retrieve articles in all journals with MSC (2000): 46L10, 46L51, 42C40
Additional Information
  • Deguang Han
  • Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816-1364
  • Email: dhan@pegasus.cc.ucf.edu
  • D. Larson
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 110365
  • Email: David.Larson@math.tamu.edu
  • Received by editor(s): February 5, 1998
  • Published electronically: April 9, 2001
  • Additional Notes: (DH) Participant, Workshop in Linear Analysis and Probability, Texas A&M University
    (DL) This work was partially supported by NSF
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 3347-3370
  • MSC (2000): Primary 46L10, 46L51, 42C40
  • DOI: https://doi.org/10.1090/S0002-9947-01-02795-7
  • MathSciNet review: 1828609