A convolution-based fractional transform

2016 ◽  
Vol 48 (8) ◽  
Author(s):  
Jiayin Dou ◽  
Qi He ◽  
Yu Peng ◽  
Qiongge Sun ◽  
Shutian Liu ◽  
...  
Keyword(s):  
Fractional Transform

Chirped double-kink and fractional-transform solitons in an optical gain medium with two-photon absorption

2014 ◽  
Vol 61 (4) ◽  
pp. 315-321 ◽  
Author(s):  
Amit Goyal ◽  
Vivek Kumar Sharma ◽  
Thokala Soloman Raju ◽  
C.N. Kumar
Keyword(s):  
Optical Gain ◽  
Gain Medium ◽  
Photon Absorption ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Double Kink ◽  
Fractional Transform

BOUNDS FOR THE EIGENVALUES OF THE FRACTIONAL LAPLACIAN

2012 ◽  
Vol 24 (03) ◽  
pp. 1250003 ◽  
Author(s):  
SELMA YILDIRIM YOLCU ◽  
TÜRKAY YOLCU
Keyword(s):  
Laplace Transform ◽  
Bounded Domain ◽  
Open Problem ◽  
Fractional Laplacian ◽  
Legendre Transform ◽  
Bounded Domains ◽  
Dirichlet Laplacian ◽  
The Laplace Transform ◽  
Fractional Transform

In this article, we extend Pólya's legendary inequality for the Dirichlet Laplacian to the fractional Laplacian. Pólya's argument is revealed to be a powerful tool for proving such extensions on tiling domains. As in the Dirichlet Laplacian case, Pólya's inequality for the fractional Laplacian on any bounded domain is still an open problem. Moreover, we also investigate the equivalence of several related inequalites for bounded domains by using the convexity, the Lieb–Aizenman procedure (the Riesz iteration), and some transforms such as the Laplace transform, the Legendre transform, and the Weyl fractional transform.

scholarly journals Discrete Pseudo-Fractional Fourier Transform and Its Fast Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (17) ◽  
pp. 2145
Author(s):  
Dorota Majorkowska-Mech ◽  
Aleksandr Cariow
Keyword(s):  
Fourier Transform ◽  
Fast Algorithm ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Composite Number ◽  
Fractional Fourier Transforms ◽  
Fractional Transform

In this article, we introduce a new discrete fractional transform for data sequences whose size is a composite number. The main kernels of the introduced transform are small-size discrete fractional Fourier transforms. Since the introduced transformation is not, in the generally known sense, a classical discrete fractional transform, we call it discrete pseudo-fractional Fourier transform. We also provide a generalization of this new transform, which depends on many fractional parameters. A fast algorithm for computing the introduced transform is developed and described.

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