IJPAM: Volume 26, No. 3 (2006)

FROM WEYL-HEISENBERG FRAMES TO
INFINITE QUADRATIC FORMS

Xunxiang Guo$^1$, Yuanan Diao$^2$, Xingde Dai$^3$
$^1$Department of Mathematics and Computer Science
Gannan Normal University
Gan Zhou, Jiangxi Province, P.R. CHINA
e-mail: guoxunxiang@yahoo.com
$^{2,3}$ Department of Mathematics and Statistics
University of North Carolina Charlotte
9201 University City Boulevard
Charlotte, NC 28223, USA
$^2$e-mail: ydiao@uncc.edu
$^3$e-mail: xdai@uncc.edu


Abstract.Let $a$, $b$ be two fixed positive constants. A function $g\in L^2({\mathbb R})$ is called a mother Weyl-Heisenberg frame wavelet for $(a,b)$ if $g$ generates a frame for $L^2({\mathbb R})$ under modulates by $b$ and translates by $a$, i.e., $\{e^{imbt}g(t-na)\}_{m,n\in\mathbb{Z}}$ is a frame for $L^2(\mathbb{R})$. In this paper, we establish a connection between mother Weyl-Heisenberg frame wavelets of certain special forms and certain strongly positive definite quadratic forms of infinite dimension. Some examples of application in matrix algebra are provided.

Received: November 10, 2006

AMS Subject Classification: 47A25

Key Words and Phrases: frames, frame wavelets, frame wavelet sets, Weyl-Heisenberg frames, infinite quadratic forms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 3