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] |
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| Database: | Engineering Source |
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