Riesz sequences of translates and generalized duals with support on [0,1]

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If the integer translates of a function phi with compact support generate a frame for a subspace W of L-2(R), then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether phi is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists.
Publisher
Springer
Issue Date
2006
Language
English
Article Type
Article
Keywords

SUBSPACES; FRAMES; BASES

Citation

JOURNAL OF GEOMETRIC ANALYSIS, v.16, no.4, pp.585 - 596

ISSN
1050-6926
DOI
10.1007/BF02922132
URI
http://hdl.handle.net/10203/89834
Appears in Collection
MA-Journal Papers(저널논문)
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