Tighter uncertainty principles associated with Bendlet and quaternion-Bendlet transforms

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 30 - 24
• Main Authors: Li, Cen, Wang, Xinyu, Zheng, Shenzhou
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 04.03.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Continuous Bendlet transform (CBT); Continuous quaternion Bendlet transform (CQBT); Data compression; Fourier transforms; Lower bounds; Mathematics; Mathematics and Statistics; Principles; Quaternions; Tighter Heisenberg-Weyl UP; Uncertainty principles; Uncertainty principles (UPs); Wavelet transforms; Continuous quaternion Bendlet transform (CQBT); 42B10; Continuous Bendlet transform (CBT); Tighter Heisenberg-Weyl UP; 30G35; 94A12; Uncertainty principles (UPs)
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-025-03277-8

This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs.