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Journals / Düzce Üniversitesi Bilim ve Teknoloji Dergisi / 2023 / Cilt: 11 Sayı: 2

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

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

Erdem TOKSOY
Pages
717–728
Publication Date
2023-04-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Kesirli Fourier dönüşümü · girişim işlemi · Wiener-tipi uzaylar

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.

Özet

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.

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Cite This Article

TOKSOY, E. (2023). A Note on Function Spaces with Fractional Fourier Transforms in Wiener-type Spaces. Düzce Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 11 Sayı: 2, 717–728. https://ajindex.com/articles/927294

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