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Resumo(s)
Quaternion Hyperbolic Transforms of the Fourier type associated with quaternion-valued signals defined over an open rectangle of the Euclidean plane endowed with a hyperbolic measure include the Fourier, Wigner-Ville, and linear canonical transforms. In this paper, we give a descriptive review of these generalized transforms and provide some of their important properties. The different forms of the hyperbolic kernels of such transforms contain hyperbolic spatial variables and frequency variables together with two quaternion algebra generators that take over the role of imaginary units (an essential feature to maintain the separation between the two dimensions).
Descrição
Part of the book series: Trends in Mathematics (TM, volume 9)
Part of the book sub series: Research Perspectives Ghent Analysis and PDE Center (RPGAPC)
Included in the following conference series:
ICHAA: International Conference on Hypercomplex Analysis and its Applications
Extended Abstracts of the International Conference Celebrating Paula Cerejeiras’ 60th Birthday
Conference proceedings © 2025
Acknowledgements: The first author’s work was supported by Portuguese funds through CIDMA – Center for Research and Development in Mathematics and Applications, and FCT – Fundação para a Ciência e a Tecnologia, within projects ˆ https://doi.org/10.54499/UIDB/04106/2020 and https://doi.org/10.54499/UIDP/04106/2020. The second author’s work was supported by the Asociación Mexicana de Cultura, A. C.
Acknowledgements: The first author’s work was supported by Portuguese funds through CIDMA – Center for Research and Development in Mathematics and Applications, and FCT – Fundação para a Ciência e a Tecnologia, within projects ˆ https://doi.org/10.54499/UIDB/04106/2020 and https://doi.org/10.54499/UIDP/04106/2020. The second author’s work was supported by the Asociación Mexicana de Cultura, A. C.
Palavras-chave
Quaternion Hyperbolic Transforms Quaternion Fourier Transform Linear Canonical Transform Wigner-Ville Transform Quaternionic Signal Analysis Hyperbolic Geometry
Contexto Educativo
Citação
Ferreira, M., Morais, J. (2025). Quaternion Hyperbolic Transforms of the Fourier Type: An Overview. In: Faustino, N., Ferreira, M., Kähler, U., Vieira, N. (eds) Hypercomplex Analysis and Its Applications. ICHAA 2024. Trends in Mathematics(), vol 9. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-86858-0_5
Editora
Springer Nature