The canonical and alternate duals of a wavelet frame

Publication: Research - peer-reviewJournal article – Annual report year: 2007

Standard

The canonical and alternate duals of a wavelet frame. / Lemvig, Jakob; Bownik, Marcin.

In: Applied and Computational Harmonic Analysis, Vol. 23, No. 2, 2007, p. 263-272.

Publication: Research - peer-reviewJournal article – Annual report year: 2007

Harvard

APA

CBE

MLA

Vancouver

Author

Lemvig, Jakob; Bownik, Marcin / The canonical and alternate duals of a wavelet frame.

In: Applied and Computational Harmonic Analysis, Vol. 23, No. 2, 2007, p. 263-272.

Publication: Research - peer-reviewJournal article – Annual report year: 2007

Bibtex

@article{d242bb25c5cd4c1197415dc3b6425428,
title = "The canonical and alternate duals of a wavelet frame",
publisher = "Academic Press",
author = "Jakob Lemvig and Marcin Bownik",
year = "2007",
doi = "10.1016/j.acha.2007.04.004",
volume = "23",
number = "2",
pages = "263--272",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",

}

RIS

TY - JOUR

T1 - The canonical and alternate duals of a wavelet frame

A1 - Lemvig,Jakob

A1 - Bownik,Marcin

AU - Lemvig,Jakob

AU - Bownik,Marcin

PB - Academic Press

PY - 2007

Y1 - 2007

N2 - We show that there exists a frame wavelet ψ with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. On the other hand, there exists infinitely many alternate duals of ψ generated by a single function. Our argument closes a gap in the original proof of this fact by Daubechies and Han [Appl. Comp. Harmonic Anal. 12 (2002), no. 3, 269 –285].

AB - We show that there exists a frame wavelet ψ with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. On the other hand, there exists infinitely many alternate duals of ψ generated by a single function. Our argument closes a gap in the original proof of this fact by Daubechies and Han [Appl. Comp. Harmonic Anal. 12 (2002), no. 3, 269 –285].

U2 - 10.1016/j.acha.2007.04.004

DO - 10.1016/j.acha.2007.04.004

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

SN - 1063-5203

IS - 2

VL - 23

SP - 263

EP - 272

ER -