On the Duality Principle by Casazza, Kutyniok, and Lammers

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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On the Duality Principle by Casazza, Kutyniok, and Lammers. / Christensen, Ole; Kim, Hong Oh; Kim, Rae Young.

In: Journal of Fourier Analysis and Applications, Vol. 17, No. 4, 2011, p. 640-655.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Author

Christensen, Ole; Kim, Hong Oh; Kim, Rae Young / On the Duality Principle by Casazza, Kutyniok, and Lammers.

In: Journal of Fourier Analysis and Applications, Vol. 17, No. 4, 2011, p. 640-655.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

Bibtex

@article{42c1793e134d4813b1ed64d2c3d6f7f4,
title = "On the Duality Principle by Casazza, Kutyniok, and Lammers",
author = "Ole Christensen and Kim, {Hong Oh} and Kim, {Rae Young}",
year = "2011",
doi = "10.1007/s00041-010-9151-4",
volume = "17",
number = "4",
pages = "640--655",
journal = "Journal of Fourier Analysis and Applications",
issn = "10695869",

}

RIS

TY - JOUR

T1 - On the Duality Principle by Casazza, Kutyniok, and Lammers

A1 - Christensen,Ole

A1 - Kim,Hong Oh

A1 - Kim,Rae Young

AU - Christensen,Ole

AU - Kim,Hong Oh

AU - Kim,Rae Young

PY - 2011

Y1 - 2011

N2 - The R-dual sequences of a frame {f i } i∈I , introduced by Casazza, Kutyniok and Lammers in (J. Fourier Anal. Appl. 10(4):383–408, 2004), provide a powerful tool in the analysis of duality relations in general frame theory. In this paper we derive conditions for a sequence {ω j } j∈I to be an R-dual of a given frame {f i } i∈I . In particular we show that the R-duals {ω j } j∈I can be characterized in terms of frame properties of an associated sequence {n i } i∈I . We also derive the duality results obtained for tight Gabor frames in (Casazza et al. in J. Fourier Anal. Appl. 10(4):383–408, 2004) as a special case of a general statement for R-duals of frames in Hilbert spaces. Finally we consider a relaxation of the R-dual setup of independent interest. Several examples illustrate the results.

AB - The R-dual sequences of a frame {f i } i∈I , introduced by Casazza, Kutyniok and Lammers in (J. Fourier Anal. Appl. 10(4):383–408, 2004), provide a powerful tool in the analysis of duality relations in general frame theory. In this paper we derive conditions for a sequence {ω j } j∈I to be an R-dual of a given frame {f i } i∈I . In particular we show that the R-duals {ω j } j∈I can be characterized in terms of frame properties of an associated sequence {n i } i∈I . We also derive the duality results obtained for tight Gabor frames in (Casazza et al. in J. Fourier Anal. Appl. 10(4):383–408, 2004) as a special case of a general statement for R-duals of frames in Hilbert spaces. Finally we consider a relaxation of the R-dual setup of independent interest. Several examples illustrate the results.

KW - Wexler-Raz theorem

KW - Gabor system

KW - Frame

KW - Riesz basis

KW - Duality principle

U2 - 10.1007/s00041-010-9151-4

DO - 10.1007/s00041-010-9151-4

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 10695869

IS - 4

VL - 17

SP - 640

EP - 655

ER -