Please use this identifier to cite or link to this item: https://doi.org/10.1007/s11856-009-0079-9
Title: Characterization of Sobolev spaces of arbitrary smoothness using nonstationary tight wavelet frames
Authors: Han, B.
Shen, Z. 
Issue Date: Aug-2009
Citation: Han, B., Shen, Z. (2009-08). Characterization of Sobolev spaces of arbitrary smoothness using nonstationary tight wavelet frames. Israel Journal of Mathematics 172 (1) : 371-398. ScholarBank@NUS Repository. https://doi.org/10.1007/s11856-009-0079-9
Abstract: In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(ℝ). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted ℓ2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L2(ℝ) derived from masks of pseudosplines in [15]. This implies that any compactly supported nonstationary tight wavelet frame of L2(ℝ) in [15] can be properly normalized into a pair of dual frames in the corresponding pair of dual Sobolev spaces of an arbitrary fixed order of smoothness. © 2009 Hebrew University Magnes Press.
Source Title: Israel Journal of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/102978
ISSN: 00212172
DOI: 10.1007/s11856-009-0079-9
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