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Stability of the Shifts of a Finite Number of Functions

โœ Scribed by Rong-Qing Jia

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
226 KB
Volume
95
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

Let , 1 , ..., , n be compactly supported distributions in L p (R s ) ( 0<p). We say that the shifts of , 1 , ..., , n are L p -stable if there exist two positive constants C 1 and C 2 such that, for arbitrary sequences a 1 , ..., a n # l p (Z s ),

In this paper we prove that the shifts of , 1 , ..., , n are L p -stable if and only if, for any ! # R s , the sequences (, k (!+2;?)) ; # Z s (k=1, ..., n) are linearly independent, where , denotes the Fourier transform of ,. This extends the previous results of Jia and Micchelli on a characterization of L p -stability (1 p ) of the shifts of a finite number of compactly supported functions to the case 0<p .

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