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|Title:||Characterization of Sobolev spaces of arbitrary smoothness using nonstationary tight wavelet frames|
|Source:||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 . This implies that any compactly supported nonstationary tight wavelet frame of L2(ℝ) in  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|
|Appears in Collections:||Staff Publications|
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