Some compact and non-compact embedding theorems for the function spaces defined by fractional Fourier transform

Authors : Erdem TOKSOY, Ayşe SANDIKÇI

Pages : 1620-1635

Doi:10.15672/hujms.795924

View : 15 | Download : 5

Publication Date : 2021-12-14

Article Type : Research Paper

Abstract :The fractional Fourier transform is a generalization of the classical Fourier transform through an angular parameter $\alpha $. This transform uses in quantum optics and quantum wave field reconstruction, also its application provides solving some differrential equations which arise in quantum mechanics. The aim of this work is to discuss compact and non-compact embeddings between the spaces $A_{\alpha ,p}^{w,\omega }\leftinsert ignore into journalissuearticles values(\mathbb{R}^{d}\right); $ which are the set of functions in ${L_{w}^{1}\leftinsert ignore into journalissuearticles values(\mathbb{R}^{d}\right); }$ whose fractional Fourier transform are in ${L_{\omega}^{p}\leftinsert ignore into journalissuearticles values(\mathbb{R}^{d}\right); }$. Moreover, some relevant counterexamples are indicated.
Keywords : Fractional Fourirer transform, weighted Lebesgue spaces, compact embedding