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Wavelet Frames for Distributions in Anisotropic Besov Spaces

Wavelet Frames for Distributions in Anisotropic Besov Spaces Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎 1 , . . . , 𝑎 𝑛 ) is an anisotropy, with 𝑎 𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎 1 + . . . + 𝑎 𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in Triebel, Studia Math. 154: 59–88, 2003. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Wavelet Frames for Distributions in Anisotropic Besov Spaces

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References (39)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2005.637
Publisher site
See Article on Publisher Site

Abstract

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎 1 , . . . , 𝑎 𝑛 ) is an anisotropy, with 𝑎 𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎 1 + . . . + 𝑎 𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in Triebel, Studia Math. 154: 59–88, 2003.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2005

Keywords: Anisotropic function spaces; sub-atomic decomposition; wavelet decomposition; wavelet frames

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