Regularity properties of Haar Frames
We prove that pointwise and global Hölder regularity can be characterized using the coefficients on the Haar tight frame obtained by using a finite union of shifted Haar bases, despite the fact that the elements composing the frame are discontinuous.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.228/ |
| _version_ | 1797651532070518784 |
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| author | Jaffard, Stéphane Krim, Hamid |
| author_facet | Jaffard, Stéphane Krim, Hamid |
| author_sort | Jaffard, Stéphane |
| collection | DOAJ |
| description | We prove that pointwise and global Hölder regularity can be characterized using the coefficients on the Haar tight frame obtained by using a finite union of shifted Haar bases, despite the fact that the elements composing the frame are discontinuous. |
| first_indexed | 2024-03-11T16:17:09Z |
| format | Article |
| id | doaj.art-47567fb287424ec9bef4ab928ac618b0 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:09Z |
| publishDate | 2021-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-47567fb287424ec9bef4ab928ac618b02023-10-24T14:19:13ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-11-0135991107111710.5802/crmath.22810.5802/crmath.228Regularity properties of Haar FramesJaffard, Stéphane0Krim, Hamid1Univ Paris Est Creteil, CNRS, LAMA, F-94010 Creteil, France, Univ Gustave Eiffel, LAMA, F-77447 Marne-la-Vallée, France.Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695 USA.We prove that pointwise and global Hölder regularity can be characterized using the coefficients on the Haar tight frame obtained by using a finite union of shifted Haar bases, despite the fact that the elements composing the frame are discontinuous.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.228/ |
| spellingShingle | Jaffard, Stéphane Krim, Hamid Regularity properties of Haar Frames Comptes Rendus. Mathématique |
| title | Regularity properties of Haar Frames |
| title_full | Regularity properties of Haar Frames |
| title_fullStr | Regularity properties of Haar Frames |
| title_full_unstemmed | Regularity properties of Haar Frames |
| title_short | Regularity properties of Haar Frames |
| title_sort | regularity properties of haar frames |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.228/ |
| work_keys_str_mv | AT jaffardstephane regularitypropertiesofhaarframes AT krimhamid regularitypropertiesofhaarframes |