IJPAM: Volume 75, No. 4 (2012)



Andrew Dugowson



Central Michigan University
Mount Pleasant, Michigan, 48859, USA

University of Wisconsin-Madison
1410, Engineering Drive, Madison, WI 53706, USA

Pomona College
333, N. College Way, Claremont, CA 91711, USA

Case Western Reserve University
Cleveland, Ohio, 44106, USA
Abstract. Let be a separable Hilbert space with inner product
. We say a set
is a (fundamental) frame for
if there exist
such that for each
,
![]() |
(1) |
In case
is a frame for the subspace
, we say that
is a frame sequence.
A Weyl-Heisenberg frame sequence is a frame sequence which is generated by translated and modulated versions of -functions.
In this paper, we characterize Weyl-Heisenberg frame sequences using infinite Hermitian matrices and obtain the optimal frame bounds in terms of the operator norms of these matrices.
This work is inspired by a paper by Casazza and Christensen, where sufficient conditions for a Weyl-Heisenberg system to be a frame sequence are studied.
Received: August 24, 2010
AMS Subject Classification: 42C15
Key Words and Phrases: frame sequences, Hermitian matrix, Weyl-Heisenberg systems, modulation frames
Download paper from here.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 4