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The Shift-Invariant Subspaces in L1(R)

โœ Scribed by Wu Zhengchang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
139 KB
Volume
118
Category
Article
ISSN
0021-9045

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In this paper, we study the reconstruction of functions in shift invariant subspaces from local averages with symmetric averaging functions. We present an average sampling theorem for shift invariant subspaces and give quantitative results on the aliasing error and the truncation error. We show that

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โœ A. Askari Hemmat; J.-P. Gabardo ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 256 KB

For an invertible nร—n matrix B and a finite or countable subset of Our main objects of interest in this paper are the kernel of the associated Gramian G(.) and dual Gramian G(.) operator-valued functions. We show in particular that the orthogonal complement of M in L 2 (R n ) can be generated by a

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For 1 p , sufficient conditions on the generators [, h ] h>0 are given which ensure that the h-dilates of the shift-invariant space generated by , h provide L p -approximation of order k>0. Examples where , h is an exponential box spline or certain dilates of the Gaussian e &| } | 2 are considered;