Article ID: MTJPAM-D-21-00034

Title: On an abstract Segal algebra under fractional convolution


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00034; Volume 4 / Issue 1 / Year 2022, Pages 1-22

Document Type: Research Paper

Author(s): Ayşe Sandıkçı a , Erdem Toksoy b

aOndokuz Mayıs University, Faculty of Art and Sciences, Departman of Mathematics, Kurupelit, Samsun, 55139, Turkey

bOndokuz Mayıs University, Faculty of Art and Sciences, Departman of Mathematics, Kurupelit, Samsun, 55139, Turkey

Received: 19 May 2021, Accepted: 18 June 2021, Published: 30 June 2021.

Corresponding Author: Ayşe Sandıkçı (Email address: ayses@omu.edu.tr)

Full Text: PDF

Abstract

In this work, we find approximate identities for the spaces  {L}^{{1}}{\left(\mathbb{R}^{d}\right)},  {L_{w}^{1}\left(\mathbb{R}^{d}\right)} and  S_{w}^{\alpha }(\mathbb{R}{^{d}})  under \Theta convolution. Furthermore, we determine approximate identities with compactly supported fractional Fourier transforms in the spaces  {L_{w}^{1}\left(\mathbb{R}^{d}\right)}  and  S_{w}^{\alpha }(\mathbb{R}{^{d}}), where  w  is weight function of regular growth. We give definitions of multipliers of these Banach algebras under  \Theta  convolution. Also, we show that the space  S_{w}^{\alpha }(\mathbb{R}{^{d}})  under some conditions is an abstract Segal algebra with recpect to  {L_{w}^{1}\left(\mathbb{R}^{d}\right)}.

Keywords: Fractional Fourier transform, approximate identity, Segal algebras

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