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Article: Classification of refinable splines
| Title | Classification of refinable splines |
|---|---|
| Authors | |
| Keywords | Quasi-trigonometric polynomial Refinable spline Spline Weierstrass factorization theorem |
| Issue Date | 2006 |
| Citation | Constructive Approximation, 2006, v. 24, n. 2, p. 187-200 How to Cite? |
| Abstract | A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well-known B-splines, play a key role in computer aided geometric design. So far all studies on refinable splines have focused on positive integer dilations and integer translations, and under this setting a rather complete classification was obtained in [12]. However, refinable splines do not have to have integer dilations and integer translations. The classification of refinable splines with noninteger dilations and arbitrary translations is studied in this paper. We classify completely all refinable splines with integer translations and arbitrary dilations. Our study involves techniques from number theory and complex analysis. © 2006 Springer Science+Business Media, Inc. |
| Persistent Identifier | http://hdl.handle.net/10722/363087 |
| ISSN | 2023 Impact Factor: 2.3 2023 SCImago Journal Rankings: 1.243 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Dai, Xin Rong | - |
| dc.contributor.author | Feng, De Jun | - |
| dc.contributor.author | Wang, Yang | - |
| dc.date.accessioned | 2025-10-10T07:44:30Z | - |
| dc.date.available | 2025-10-10T07:44:30Z | - |
| dc.date.issued | 2006 | - |
| dc.identifier.citation | Constructive Approximation, 2006, v. 24, n. 2, p. 187-200 | - |
| dc.identifier.issn | 0176-4276 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/363087 | - |
| dc.description.abstract | A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well-known B-splines, play a key role in computer aided geometric design. So far all studies on refinable splines have focused on positive integer dilations and integer translations, and under this setting a rather complete classification was obtained in [12]. However, refinable splines do not have to have integer dilations and integer translations. The classification of refinable splines with noninteger dilations and arbitrary translations is studied in this paper. We classify completely all refinable splines with integer translations and arbitrary dilations. Our study involves techniques from number theory and complex analysis. © 2006 Springer Science+Business Media, Inc. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Constructive Approximation | - |
| dc.subject | Quasi-trigonometric polynomial | - |
| dc.subject | Refinable spline | - |
| dc.subject | Spline | - |
| dc.subject | Weierstrass factorization theorem | - |
| dc.title | Classification of refinable splines | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1007/s00365-005-0622-9 | - |
| dc.identifier.scopus | eid_2-s2.0-33745291457 | - |
| dc.identifier.volume | 24 | - |
| dc.identifier.issue | 2 | - |
| dc.identifier.spage | 187 | - |
| dc.identifier.epage | 200 | - |
| dc.identifier.eissn | 1432-0940 | - |