Oversampling of wavelet frames for real dilations

Marcin Bownik; Jakob Lemvig

doi:10.1112/jlms/jdr067

Oversampling of wavelet frames for real dilations

Marcin Bownik, Jakob Lemvig

University of Oregon

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Abstract

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

Original language	English
Journal	Journal of the London Mathematical Society
Volume	85
Issue number	3
Pages (from-to)	765-788
ISSN	0024-6107
DOIs	https://doi.org/10.1112/jlms/jdr067
Publication status	Published - 2012

Keywords

Transversal constellation
Second Oversampling Theorem
Real dilations
Approximate dual lattice
Affine frames
Shift invariant subspaces
Wavelets
Approximate transversal
Lattice

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title = "Oversampling of wavelet frames for real dilations",

abstract = "We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.",

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AU - Lemvig, Jakob

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AB - We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

KW - Transversal constellation

KW - Second Oversampling Theorem

KW - Real dilations

KW - Approximate dual lattice

KW - Affine frames

KW - Shift invariant subspaces

KW - Wavelets

KW - Approximate transversal

KW - Lattice

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DO - 10.1112/jlms/jdr067

M3 - Journal article

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VL - 85

SP - 765

EP - 788

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

Oversampling of wavelet frames for real dilations

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Keywords

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