Quarkonial frames with compression properties.
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| Title: | Quarkonial frames with compression properties. |
|---|---|
| Authors: | Dahlke, Stephan1, Keding, Philipp1 keding@mathematik.uni-marburg.de, Raasch, Thorsten2 |
| Source: | Calcolo. Sep2017, Vol. 54 Issue 3, p823-855. 33p. |
| Subjects: | Frames (Combinatorial analysis), Longitudinal waves, Function spaces, Sobolev spaces, Mathematical decomposition, Partition of unity method |
| Abstract: | In the spirit of subatomic or quarkonial decomposition of function spaces (Triebel in Fractals and spectra related to fourier analysis and function spaces. Birkhäuser, Boston, 1997), we construct compactly supported, piecewise polynomial functions whose properly weighted dilates and translates generate frames for Sobolev spaces on the real line. All frame elements except for those on the coarsest level have vanishing moment properties. As a consequence, the matrix representation of certain elliptic operators in frame coordinates is compressible, i.e., well-approximable by sparse submatrices. [ABSTRACT FROM AUTHOR] |
| Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 125842672 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quarkonial frames with compression properties. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Dahlke%2C+Stephan%22">Dahlke, Stephan</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Keding%2C+Philipp%22">Keding, Philipp</searchLink><relatesTo>1</relatesTo><i> keding@mathematik.uni-marburg.de</i><br /><searchLink fieldCode="AR" term="%22Raasch%2C+Thorsten%22">Raasch, Thorsten</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Calcolo%22">Calcolo</searchLink>. Sep2017, Vol. 54 Issue 3, p823-855. 33p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Frames+%28Combinatorial+analysis%29%22">Frames (Combinatorial analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Longitudinal+waves%22">Longitudinal waves</searchLink><br /><searchLink fieldCode="DE" term="%22Function+spaces%22">Function spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Sobolev+spaces%22">Sobolev spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+decomposition%22">Mathematical decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the spirit of subatomic or quarkonial decomposition of function spaces (Triebel in Fractals and spectra related to fourier analysis and function spaces. Birkhäuser, Boston, 1997), we construct compactly supported, piecewise polynomial functions whose properly weighted dilates and translates generate frames for Sobolev spaces on the real line. All frame elements except for those on the coarsest level have vanishing moment properties. As a consequence, the matrix representation of certain elliptic operators in frame coordinates is compressible, i.e., well-approximable by sparse submatrices. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10092-016-0210-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 33 StartPage: 823 Subjects: – SubjectFull: Frames (Combinatorial analysis) Type: general – SubjectFull: Longitudinal waves Type: general – SubjectFull: Function spaces Type: general – SubjectFull: Sobolev spaces Type: general – SubjectFull: Mathematical decomposition Type: general – SubjectFull: Partition of unity method Type: general Titles: – TitleFull: Quarkonial frames with compression properties. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Dahlke, Stephan – PersonEntity: Name: NameFull: Keding, Philipp – PersonEntity: Name: NameFull: Raasch, Thorsten IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 00080624 Numbering: – Type: volume Value: 54 – Type: issue Value: 3 Titles: – TitleFull: Calcolo Type: main |
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