IJPAM: Volume 6, No. 2 (2003)

MULTIWAVELETS ASSOCIATED WITH COUNTABLE
GROUPS OF UNITARY OPERATORS
IN HILBERT SPACES

D.R. Larson$^1$, W.S. Tang$^2$, E. Weber$^3$
$^1$Department of Mathematics
Texas A&M University
College Station, TX 77843-3368, USA
e-mail: larson@math.tamu.edu
$^2$Department of Mathematics
National University of Singapore
Science Drive 2, 117543, REPUBLIC OF SINGAPORE
e-mail: mattws@math.nus.edu.sg
$^3$Department of Mathematics
University of Wyoming
Laramie, WY 82071-3036, USA
e-mail: esw@uwyo.edu


Abstract.Let ${\cal G}$ be a countable group of unitary operators on a complex separable Hilbert space $H$. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.

Received: February 27, 2003

AMS Subject Classification: 46C99, 47B99, 46B15

Key Words and Phrases: biorthogonal systems, Riesz bases, multiwavelets, unitary operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 2