Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = Littlewood–Paley theorem

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
22 pages, 3367 KB  
Article
2D Linear Canonical Transforms on Lp and Applications
by Yinuo Yang, Qingyan Wu and Seong-Tae Jhang
Fractal Fract. 2023, 7(2), 100; https://doi.org/10.3390/fractalfract7020100 - 17 Jan 2023
Cited by 6 | Viewed by 2171
Abstract
As Fourier transformations of Lp functions are the mathematical basis of various applications, it is necessary to develop Lp theory for 2D-LCT before any further rigorous mathematical investigation of such transformations. In this paper, we study this Lp theory for [...] Read more.
As Fourier transformations of Lp functions are the mathematical basis of various applications, it is necessary to develop Lp theory for 2D-LCT before any further rigorous mathematical investigation of such transformations. In this paper, we study this Lp theory for 1p<. By defining an appropriate convolution, we obtain a result about the inverse of 2D-LCT on L1(R2). Together with the Plancherel identity and Hausdorff–Young inequality, we establish Lp(R2) multiplier theory and Littlewood–Paley theorems associated with the 2D-LCT. As applications, we demonstrate the recovery of the L1(R2) signal function by simulation. Moreover, we present a real-life application of such a theory of 2D-LCT by encrypting and decrypting real images. Full article
(This article belongs to the Special Issue Recent Advances in Fractional Fourier Transforms and Applications)
Show Figures

Figure 1

Back to TopTop