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Abstract
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| The aim of this paper is to derive stable generalized sampling in a shift-invariant space with n stable generators. This is done in the light of the theory of frames in the product Hilbert space L^2_n(0,1):=L^2(0,1)x¿..xL^2(0,1) (n times). The generalized samples are expressed as the frame coefficients of an appropriate function in L^2_n(0,1) with respect to some particular frame in L^2_n(0,1). Since any multiply stable generated shift-invariant space is the image of L^2_n(0,1) by means of a bounded invertible operator, the generalized sampling is obtained from some dual frame expansions in L^2_n(0,1). An example in the setting of the Hermite cubic splines is exhibited. | |
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International
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Si |
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JCR
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Si |
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Title
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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
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ISBN
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0022-247X |
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Impact factor JCR
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0,872 |
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Impact info
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Volume
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237 |
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10.1016/j.jmaa.2007.03.083 |
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Journal number
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1 |
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From page
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69 |
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To page
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84 |
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Month
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ENERO |
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Ranking
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