Abstract
The set of all orthogonal multiwavelets with multiresolution analysis of multiplicity r in L(R ) is parameterized by a set of unitary operators which satisfies certain commutative properties. The parameterization of frame multiwavelets with multiresolution analysis of multiplicity r is discussed by a set of co-isometry operators, and the Riesz multiwavelets with multiresolution analysis is obtained by a set of invertible operators. AMS Subject Classification: 42C40, 46C05, 47B38
Highlights
Let H be a separable complex Hilbert space and B(H) deonote the algebra of all bounded linear operators on H
We call A, B the lower and upper frame bounds for the frame, respectively
The frame is called a tight frame if A = B, and is called a normalized frame if A = B = 1
Summary
Let H be a separable complex Hilbert space and B(H) deonote the algebra of all bounded linear operators on H. Otherwords, the authors of [20, 21, 22] parametrized the set of single orthonormal wavelets by unitary operators in Cψ0(D, T ). We will study the local commutant theory of multiwavelet (Parseval frame multiwavelet, Riesz multiwavelet) with multiplicity r with MRA. An orthonormal (or a Parseval frame, a Riesz) multiresolution analysis of multiplicity r (r-MRA) (or a r-FMRA, a r-RMRA) in H is a set {Vn : n ∈ Z} of closed subspaces in H satisfying the following properties:. An orthonormal multiwavelet (or a Parseval frame multiwavelet, a Riesz multiwavelet) with multiplicity r Ψ = (ψ1(t), · · · , ψr(t)) with ψi ∈ W0 = V1 ⊖ V0, i = 1, · · · , r can be from a r-MRA (or a r-FMRA, a r-RMRA), see [1, 2].
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