Let w and ω be weight functions on R d . In this work, we define A with convolution operation. At the end of this work, we discuss inclusion properties of these spaces.
The purpose of this paper is to introduce and study a function space A_(α,w)^(B,Y) (R^d ) to be a linear space of functions h∈L_w^1 (R^d ) whose fractional Fourier transforms F_α h belong to the Wiener-type space W(B,Y)(R^d ), where w is a Beurling weight function on R^d. We show that this space becomes a Banach algebra with the sum norm 〖‖h‖〗_(1,w)+〖‖F_α h‖〗_(W(B,Y)) and Θ convolution operation under some conditions. We find an approximate identity in this space and show that this space is an abstract Segal algebra with respect to L_w^1 (R^d ) under some conditions.
In this study, first of all we define spaces () d S and () d w S and give examples of these spaces. After we w L uzayının bir Banach ideali olduğu gösterildi. Ayrıca () d w S uzayının öteleme ve karakter işlemcileri altında değişmez olduğu ve bu operatörlerin sürekliliği ispatlandı. Son olarak bu uzayların kapsama özellikleri tartışıldı.
The fractional Fourier transform is a generalization of the classical Fourier transform through an angular parameter α. This transform uses in quantum optics and quantum wave field reconstruction, also its application provides solving some differential equations which arise in quantum mechanics. The aim of this work is to discuss compact and non-compact embeddings between the spaces A w,ω α,p R d which are the set of functions in L 1 w R d whose fractional Fourier transform are in L p ω R d . Moreover, some relevant counterexamples are indicated.
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