# A characterization of L-dual frames and L-dual Riesz bases

Document Type : Research Paper

Authors

Abstract

This paper is an investigation of $L$-dual frames with respect
to a function-valued inner product, the so called $L$-bracket
product on $L^{2}(G)$, where G is a locally compact abelian group
with a uniform lattice $L$. We show that several well known theorems
for dual frames and dual Riesz bases in a Hilbert space
remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

Keywords

### History

• Receive Date: 06 November 2009
• Revise Date: 09 March 2012
• Accept Date: 04 April 2010
• First Publish Date: 15 September 2011