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Tight frames of compactly supported affine wavelets (1990)

Lawton, Wayne M.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 31 (1990), S. 1898-1901

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: This paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by Daubechies [Commun. Pure Appl. Math. 41, 909 (1988)]. For each integer N≥1, a family of wavelet functions ψ having support [0,2N−1] is constructed such that {ψjk(x)=2j/2ψ(2jx−k) kj,k∈Z} is a tight frame of L2(R), i.e., for every f∈L2(R), f=c∑jk 〈ψjk||f〉ψjk for some c〉0. This family is parametrized by an algebraic subset VN of R4N. Furthermore, for N≥2, a proper algebraic subset WN of VN is specified such that all points in VN outside of WN yield orthonormal bases. The relationship between these tight frames and the theory of group representations and coherent states is discussed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.528688

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