𝒪 α -transformation and its uncertainty principles
Abstract
In this paper, we introduce a family of integral transforms, denoted by Oα, and construct via kernel fusion of the fractional Fourier transform (FRFT) with angle α∉πZ. We demonstrate that the Oα-transformation constitutes a well-defined integral operator by establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the Oα-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, Pitt's inequality, and Beurling-Hörmander's theorem.
Fields of Study & Subjects
Seismic Imaging and Inversion Techniques
Geophysics and Sensor Technology
Publication details
- Journal / source
- Integral Transforms and Special Functions
- Publisher
- Informa UK Limited
- Pages
- 1–17
- Publication date
- 4 March 2026
- Language
- EN