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01.09.2017

Quarkonial frames with compression properties

verfasst von: Stephan Dahlke, Philipp Keding, Thorsten Raasch

Erschienen in: Calcolo | Ausgabe 3/2017

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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.

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Titel: Quarkonial frames with compression properties
verfasst von: Stephan Dahlke
Philipp Keding
Thorsten Raasch
Publikationsdatum: 01.09.2017
Verlag: Springer Milan
Erschienen in: Calcolo / Ausgabe 3/2017
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-016-0210-3

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