Fractional Integral Transforms: Theory and Applications presents over twenty-five integral transforms, many of which have never before been collected in one single volume. Some transforms are classic, such as Laplace, Fourier, etc, and some are relatively new, such as the Fractional Fourier, Gyrator, Linear Canonical, Special Affine Fourier Transforms, as well as, continuous Wavelet, Ridgelet, and Shearlet transforms.
The book provides an overview of the theory of fractional integral transforms with examples of such transforms, before delving deeper into the study of important fractional transforms, including the fractional Fourier transform. Applications of fractional integral transforms in signal processing and optics are highlighted. The book’s format has been designed to make it easy for readers to extract the essential information they need to learn the about the fundamental properties of each transform. Supporting proofs and explanations are given throughout.
Features
- Brings together integral transforms never before collected into a single volume
- A useful resource on fractional integral transforms for researchers and graduate students in mathematical analysis, applied mathematics, physics and engineering
- Written in an accessible style with detailed proofs and emphasis on providing the reader with an easy access to the essential properties of important fractional integral transforms
Ahmed I. Zayed is a Professor of Mathematics at the Department of Mathematical Sciences, DePaul University, Chicago, and was the Chair of the department for 20 years, from 2001 until 2021. His research interests varied over the years starting with generalized functions and distributions to sampling theory, applied harmonic analysis, special functions and integral transforms. He has published two books and edited seven research monographs. He has written 22 book chapters, published 118 research articles, and reviewed 173 publications for the Mathematical Review and 81 for the Zentralblatt für Mathematik (zbMath). He has served on the Editorial Boards of 22 scientific research journals and has refereed over 200 research papers submitted to prestigious journals, among them are IEEE, SIAM, Amer. Math. Soc., Math Physics, and Optical Soc. Journals.
1. Introduction and Preliminaries. 2. Integral Transformations. 3. Fractional Integral Transforms. 4. The Fractional Fourier Transform. 5. Shift–Invariant and Sampling Spaces of the Fractional Fourier Transform. 6. Two-Dimensional Coupled Fractional Fourier Transform. 7. The Two-Dimensional Fractional Fourier Transform and
Wigner Distribution. 8. Short-time Coupled Fractional Fourier Transform and Uncertainty Relations. 9. The Linear Canonical Transform (LCT). 10. The Special Affine Fourier Transform.
Biography
Ahmed I. Zayed is a Professor of Mathematics at the Department of Mathematical Sciences, DePaul University, Chicago, and was the Chair of the department for twenty years, from 2001 until 2021. His research interests varied over the years starting with generalized functions and distributions to sampling theory, applied harmonic analysis, special functions and integral transforms. He has published two books and edited seven research monographs. He has written 22 book chapters, published 118 research articles, and reviewed 173 publications for the Mathematical Review and 81 for the Zentralblatt für Mathematik (zbMath). He has served on the Editorial Boards of 22 scientific research journals and has refereed over 200 research papers submitted to prestigious journals, among them are IEEE, SIAM, Amer. Math. Soc., Math Physics, and Optical Soc. Journals.
