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- Title
The linear canonical wavelet transform on some function spaces.
- Authors
Guo, Yong; Li, Bing-Zhao
- Abstract
It is well known that the domain of Fourier transform (FT) can be extended to the Schwartz space for convenience. As a generation of FT, it is necessary to detect the linear canonical transform (LCT) on a new space for obtaining the similar properties like FT on . Therefore, a space generalized from is introduced firstly, and further we prove that LCT is a homeomorphism from onto itself. The linear canonical wavelet transform (LCWT) is a newly proposed transform based on the convolution theorem in LCT domain. Moreover, we propose an equivalent definition of LCWT associated with LCT and further study some properties of LCWT on . Based on these properties, we finally prove that LCWT is a linear continuous operator on the spaces of and .
- Subjects
WAVELET transforms; FUNCTION spaces; LINEAR operators; HOMEOMORPHISMS; FOURIER transforms; SCHWARTZ spaces
- Publication
International Journal of Wavelets, Multiresolution & Information Processing, 2018, Vol 16, Issue 1, p-1
- ISSN
0219-6913
- Publication type
Article
- DOI
10.1142/S0219691318500108