Shift-Invariant Spaces and Linear Operator Equations
نویسنده
چکیده
In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier transforms and semi-convolutions are used to characterize shift-invariant spaces. Criteria are provided for solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The results are then applied to the study of local shift-invariant spaces. Moreover, the approximation order of a local shift-invariant space is characterized under some mild conditions on the generators. AMS Subject Classifications: 41 A 15, 41 A 25, 41 A 63, 42 C 99, 46 E 30, 39 A 12 † Supported in part by NSERC Canada under Grant OGP 121336 Shift-Invariant Spaces and Linear Operator Equations
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تاریخ انتشار 1998