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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Wavelets in wandering subspaces


Authors: T. N. T. Goodman, S. L. Lee and W. S. Tang
Journal: Trans. Amer. Math. Soc. 338 (1993), 639-654
MSC: Primary 42C15; Secondary 41A15, 47B38
MathSciNet review: 1117215
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Abstract: Mallat's construction, via a multiresolution approximation, of orthonormal wavelets generated by a single function is extended to wavelets generated by a finite set of functions. The connection between multiresolution approximation and the concept of wandering subspaces of unitary operators in Hilbert space is exploited in the general setting. An example of multiresolution approximation generated by cardinal Hermite $ B$-splines is constructed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1117215-0
PII: S 0002-9947(1993)1117215-0
Keywords: Wavelets, Hilbert space, wandering subspaces, unitary operators, Hermite $ B$-splines
Article copyright: © Copyright 1993 American Mathematical Society