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• W2011460584 abstract "In this paper, we show that the property of tight affine frame decomposition of functions in L 2 can be extended in a stable way to functions in Sobolev spaces when the generators of the tight affine frames satisfy certain mild regularity and vanishing moment conditions. Applying the affine frame operators Q j on j th levels to any function f in a Sobolev space reveals the detailed information Q j f of f in such tight affine decompositions. We also study certain basic properties of the range of the affine frame operators Q j such as the topological property of closedness and the notion of angles between the ranges for different levels, and thus establishing some interesting connection to (tight) frames of shift-invariant spaces." @default.
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• W2011460584 date "2006-01-01" @default.
• W2011460584 modified "2023-09-29" @default.
• W2011460584 title "Affine frame decompositions and shift-invariant spaces" @default.
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• W2011460584 doi "https://doi.org/10.1016/j.acha.2005.09.003" @default.
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