Abstract
In this present work, we generalize Titchmarsh’s theorem for the complex- or hypercomplex-valued functions. Firstly, we examine the order of magnitude of the windowed linear canonical transform (WLCT) of complex-valued functions that achieved certain Lipschitz conditions on \({\mathbb {R}}\). Secondly, we studied the order of magnitude of the 2-D continuous quaternion wavelet transform (CQWT) of certain quaternionic valued Lipschitz functions.
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Bouhlal, A., Safouane, N., Achak, A. et al. Wavelet Transform of Dini Lipschitz Functions on the Quaternion Algebra. Adv. Appl. Clifford Algebras 31, 8 (2021). https://doi.org/10.1007/s00006-020-01112-5
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DOI: https://doi.org/10.1007/s00006-020-01112-5
Keywords
- Complex-valued function
- Windowed linear canonical transform
- Quaternion algebra
- Admissible quaternion wavelet