Paper Info
Title
Signal Representations Via Sip P-Frames And Sip Bessel Multipliers In Separable Banach Spaces
Abstract
Digital signals are often modeled as functions in Banach spaces, such as the ubiquitous Lp spaces. The frame theory in Banach spaces induces flexible representations of signals due to the robustness and redundancy of frames. Nevertheless, the lack of inner product in general Banach spaces limits the direct representations of signals in Banach spaces under a given basis or frame. In this paper, we introduce the concept of semi-inner product (SIP) (p,q)-Bessel multipliers to extend the flexibility of signal representations in separable Banach spaces, where 1/p + 1/q = 1, 1 < p < +infinity. These multipliers are defined as composition of analysis operator of an SIP-I Bessel sequence, a multiplication with a fixed sequence and synthesis operator of an SIP-II Bessel sequence. The basic properties of the SIP (p,q)-Bessel multipliers are investigated. Moreover, as special cases, characterizations of q-Riesz bases related to signal representations are given, and the multipliers for q-Riesz bases are discussed. We show that SIP (p,q)-Bessel multipliers for q-Riesz bases are invertible. Finally, the continuity of SIP (p,q)-Bessel multipliers with respect to their parameters is investigated. The results theoretically show that the SIP (p,q)-Bessel multipliers offer a larger range of freedom than frames on signal representations in Banach spaces.
Year
DOI
Venue
2021
10.1142/S0219691321500053
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
Keywords
DocType
Volume
Semi-inner product, SIP-I(SIP-II) p-frames, SIP-I(SIP-II) p-Bessel sequences, q-Riesz basis, SIP (p, q)-Bessel multipliers
Journal
19
Issue
ISSN
Citations 
04
0219-6913
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Xianwei Zheng101.35
Cuiming Zou222.05
Shouzhi Yang300.34