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- Publisher Website: 10.1016/j.acha.2012.06.002
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Article: The regularity of refinable functions
| Title | The regularity of refinable functions |
|---|---|
| Authors | |
| Keywords | Iterated functions system Refinable function Refinement equation Regularity of refinable functions |
| Issue Date | 2013 |
| Citation | Applied and Computational Harmonic Analysis, 2013, v. 34, n. 1, p. 142-147 How to Cite? |
| Abstract | The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias (1991) [6] states that a compactly supported refinable function in R of finite mask with integer dilation and translations cannot be in C∞. A bound on the regularity based on the eigenvalues of certain matrices associated with the refinement equation is also given. Surprisingly this fundamental classical result has not been proved in more general settings, such as in higher dimensions or when the dilation is not an integer. In this paper we extend this classical result to the most general setting for arbitrary dimension, dilation and translations. © 2012 Elsevier Inc. All rights reserved. |
| Persistent Identifier | http://hdl.handle.net/10722/363165 |
| ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 2.231 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Wang, Yang | - |
| dc.contributor.author | Xu, Zhiqiang | - |
| dc.date.accessioned | 2025-10-10T07:44:57Z | - |
| dc.date.available | 2025-10-10T07:44:57Z | - |
| dc.date.issued | 2013 | - |
| dc.identifier.citation | Applied and Computational Harmonic Analysis, 2013, v. 34, n. 1, p. 142-147 | - |
| dc.identifier.issn | 1063-5203 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/363165 | - |
| dc.description.abstract | The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias (1991) [6] states that a compactly supported refinable function in R of finite mask with integer dilation and translations cannot be in <sup>C∞</sup>. A bound on the regularity based on the eigenvalues of certain matrices associated with the refinement equation is also given. Surprisingly this fundamental classical result has not been proved in more general settings, such as in higher dimensions or when the dilation is not an integer. In this paper we extend this classical result to the most general setting for arbitrary dimension, dilation and translations. © 2012 Elsevier Inc. All rights reserved. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Applied and Computational Harmonic Analysis | - |
| dc.subject | Iterated functions system | - |
| dc.subject | Refinable function | - |
| dc.subject | Refinement equation | - |
| dc.subject | Regularity of refinable functions | - |
| dc.title | The regularity of refinable functions | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1016/j.acha.2012.06.002 | - |
| dc.identifier.scopus | eid_2-s2.0-84867396407 | - |
| dc.identifier.volume | 34 | - |
| dc.identifier.issue | 1 | - |
| dc.identifier.spage | 142 | - |
| dc.identifier.epage | 147 | - |
| dc.identifier.eissn | 1096-603X | - |