Kesirli Fourier Dönüşümleri Wiener-tipi Uzaylarda olan Fonksiyon Uzayları Üzerine Bir Not

Year 2023, Volume: 11 Issue: 2, 717 - 728, 30.04.2023

Erdem Toksoy

https://doi.org/10.29130/dubited.1068024

Abstract

Bu çalışmanın amacı w, R^d kümesi üzerinde bir Beurling ağırlık fonksiyonu olmak üzere F_α h kesirli Fourier dömüşümü W(B,Y)(R^d ) Wiener-tipi uzayına ait h∈L_w^1 (R^d ) fonksiyonlarının bir vektör uzayı olan A_(α,w)^(B,Y) (R^d ) fonksiyon uzayını tanıtmak ve çalışmaktır. Bu uzayın bazı koşullar altında, 〖‖h‖〗_(1,w)+〖‖F_α h‖〗_(W(B,Y)) toplam normu ve Θ girişim işlemiyle birlikte bir Banach cebiri olduğu gösterildi. Bu uzayda bir yaklaşık birim bulundu ve bu uzayın L_w^1 (R^d ) uzayına göre bir soyut Segal cebiri olduğu gösterildi.

Keywords

Kesirli Fourier dönüşümü, girişim işlemi, Wiener-tipi uzaylar

A Note on Function Spaces with Fractional Fourier Transforms in Wiener-type Spaces

Abstract

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.

Keywords

Fractional Fourier transform, convolution, Wiener-type spaces

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