Pairs of oblique duals in spaces of periodic functions

Christensen, Ole; Goh, Say Song

doi:10.1007/s10444-009-9115-x

Cited by 6 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Frame-like expansions have been developed and used in a wide range of disciplines. Oblique dual frames were suggested and further developed in [31][32][33][34][35][36][37]. They have properties that are very similar to those of the conventional dual frames.…”

Section: Let mentioning

confidence: 97%

“…Akinlar and Gabardo in [35] obtained a similar result for L 2 ( ) subspace Gabor frames with rational product of lattice parameters. Christensen and Goh in [37] constructed non-tight frames in finite-dimensional spaces consisting of periodic functions, and presented a setup which enables one to obtain explicit constructions of some particular convenient oblique duals.…”

Section: Let mentioning

confidence: 99%

See 1 more Smart Citation

Super Oblique Gabor Duals of Super Gabor Frames on Discrete Periodic Sets

Lian¹,

Li²

2013

Numerical Functional Analysis and Optimization

View full text Add to dashboard Cite

The notion of superframe in general Hilbert spaces was introduced in the context of multiplexing, which has been widely used in mobile communication network, satellite communication network and computer area network. The notion of oblique dual frame is a generalization of conventional dual frame. It has provided us with a frame-like expansion. Using oblique dual frames one can extend frame expansions to include redundant expansions in which the analysis and synthesis frames lie in different spaces. Given positive integers L, M and N , an N -periodic set in , let (g, N , M ) be a frame for l 2 ( , L ), and let (h, N , M ) be a frame for (h, N , M ) (generated by (h, N , M )). This article addresses super Gabor duals of g in (h, N , M ). We obtain a necessary and sufficient condition on h admitting super oblique Gabor duals of g, and present a parametrization expression of all super oblique Gabor duals and all oblique canonical Gabor duals of g. We also characterize the uniqueness of super oblique Gabor dual and oblique canonical Gabor dual of g. Some examples are also provided.

show abstract

Section: Let mentioning

confidence: 97%

Section: Let mentioning

confidence: 99%

Super Oblique Gabor Duals of Super Gabor Frames on Discrete Periodic Sets

Lian¹,

Li²

2013

Numerical Functional Analysis and Optimization

View full text Add to dashboard Cite

show abstract

“…The existence of generators satisfying (1.1) was studied in [20], see also [19] for the one-dimensional case. The construction of Parseval (multi)wavelet frames of periodic functions was carried out in [20,21,23,25] by an approach based on polyphase splines [10,11] with analysis on frequency domain. Our results are obtained from tools borrowed from the theory of shift invariant frames [7,28,29,30] which we suitably adopt to the study of Z s -periodic multiwavelet frames.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of dual multiwavelet frames of periodic functions

Atreas

2016

Int. J. Wavelets Multiresolut Inf. Process.

View full text Add to dashboard Cite

We prove characterizations of dual multiwavelet frames for [Formula: see text] constructed from a pair of [Formula: see text]-periodic multirefinable generators. Based on the notion of the Mixed Fundamental sequence we derive Mixed Extension Principles dictating the construction of dual wavelet masks with respect to given refinement masks and we show that these Principles characterize dual framelets.

show abstract