Israel Journal of Mathematics

, Volume 103, Issue 1, pp 259-288

Shift-invariant spaces and linear operator equations

  • Rong-Qing JiaAffiliated withDepartment of Mathematics, University of Alberta Email author 

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In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier trans-forms 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.