Convolution theorem and uncertainty principles for the windowed linear canonical Lions transform

Authors

  • Abdelaali Dades Department of Mathematics, Faculty of Sciences Aīn Chock, Hassan II University, Casablanca, Morocco
  • Othman Tyr Higher School of Education and Training, Ibnou Zohr University, Agadir, Morocco

DOI:

https://doi.org/10.3842/umzh.v78i3-4.9384

Keywords:

Linear canonical transform,, Linear canonical Lions transform, Generalized Fourier transform,, Convolution theorem, Uncertainty principle, kentropy

Abstract

UDC 517.44

We introduce the windowed linear canonical Lions transform, which generalizes the classical Lions transform introduced in [K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl.  Comput. Harmon. Anal., 4, № 1, 97–112 (1997)]. Some basic properties, such as Plancherel, inversion, and convolution theorems involving this integral operator are formulated and proved. In addition, the Donoho–Stark uncertainty principle, the Lieb uncertainty principle, and the Heisenberg-type inequality via the $k$-entropy are discussed and proved for the proposed transform. 

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 3-4, 2026.

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Published

28.03.2026

Issue

Vol. 78 No. 3-4 (2026)

Section

Research articles