Wavelets of multiplicity

Authors:
T. N. T. Goodman and S. L. Lee

Journal:
Trans. Amer. Math. Soc. **342** (1994), 307-324

MSC:
Primary 41A15; Secondary 41A30, 42C05, 42C15

MathSciNet review:
1232187

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Abstract | References | Similar Articles | Additional Information

Abstract: A multiresolution approximation of is of multiplicity if there are *r* functions whose translates form a Riesz basis for . In the general theory we derive necessary and sufficient conditions for the translates of to form a Riesz basis for . The resulting reconstruction and decomposition sequences lead to the construction of dual bases for and its orthogonal complement in . The general theory is applied in the construction of spline wavelets with multiple knots. Algorithms for the construction of these wavelets for some special cases are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1232187-7

Keywords:
Wavelets,
multiplicity,
decomposition and reconstruction algorithms,
duality principle,
Riesz basis,
cardinal splines with multiple knots

Article copyright:
© Copyright 1994
American Mathematical Society