Uncertainty inequalities associated with the Linear Canonical Fourier-Jacobi Wavelet Transform
Fatima Elgadiri, Abdellatif Akhlidj, Ahmed Saoudi · HAL (Le Centre pour la Communication Scientifique Directe) · 2025
In this work, we develop a comprehensive analysis of the Linear Canonical Fourier-Jacobi Wavelet Transform (LCFJWT). We begin by constructing its reproducing kernel Hilbert space structure, providing the foundation for subsequent results. Building on this framework, we establish several inequalities, including a Lieb-type bound for the continuous LCFJWT. Furthermore, we prove a Donoho-Stark type uncertainty principle, followed by a Heisenberg-type inequality, and conclude with an entropy-based uncertainty principle. These findings extend classical time-frequency-scale limitations to the Jacobi-linear canonical setting, offering new tools for harmonic analysis and potential applications in signal processing and mathematical physics.