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Quaternion algebra-valued wavelet transform. (English) Zbl 1247.42032

The author considers the continuous quaternion wavelet transform of a quaternion-valued bivariate \(L^2\)-function, which was studied in [M. Bahri, R. Ashino and R. Vaillancourt, Appl. Math. Comput. 218, No. 1, 10 – 21 (2011; Zbl 1232.65192)]. He gives an alternative proof for the inner product relation of the continuous quaternion wavelet transform.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
15A66 Clifford algebras, spinors
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Citations:

Zbl 1232.65192
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