On Some Properties of Space  S_{w}^{α}

Erdem TOKSOY; Ayşe SANDIKÇI

Article Details

On Some Properties of Space S_{w}^{α}

Authors:

Erdem TOKSOY | Ayşe SANDIKÇI

Publisher:

Erzincan Binali Yildirim University

Main Topics:

Applied physics

Journal:

Erzincan University Journal of Science and Technology 2020 Vol.13 Issue 2, pp.923-934

Document Type:

Article

Publication Date:

8/2020

Document Language:

Turkish

Document ID (Org No.):

2000414595

eISSN:

2149-4584

pISSN:

1307-9085

Abstract:

 


In this study, first of all we define spaces ( ) d S and ( ) dw S and give examples of these spaces. After wedefine ( ) dw S to be the vector space of 1( ) df Lw such that the fractional Fourier transform F f  belongsto ( ) dw S . We endow this space with the sum normSw 1,w Swf f F f      and then show that it is aBanach space. We show that ( ) dw Sis a Banach algebra and a Banach ideal on   1 dw L if the space( ) dw S is solid. Furthermore, we prove that the space ( ) dw S is translation and character invaryant andalso these operators are continuous. Finally, we discuss inclusion properties of these spaces.

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In this study, first of all we define spaces S^{Θ}(ℝ^{d}) and S_{w}^{Θ}(ℝ^{d}) and give examples
of these spaces. After we define S_{w}^{α}(ℝ^{d}) to be the vector
space of f∈L_{w}¹(ℝ^{d}) such that the
fractional Fourier transform F_{α}f belongs to S_{w}^{Θ}(ℝ^{d}). We endow this space with the sum norm ‖f‖_{S_{w}^{α}}=‖f‖_{1,w}+‖F_{α}f‖_{S_{w}^{Θ}} and then show
that it is a Banach space. We show that S_{w}^{α}(ℝ^{d}) is a Banach algebra and a Banach ideal on L_{w}¹(ℝ^{d}) if the space  S_{w}^{Θ}(ℝ^{d}) is solid. Furthermore, we proof that the space S_{w}^{α}(ℝ^{d}) is translation
and character invaryant and also these operators are continuous. Finally, we
discuss inclusion properties of these spaces.

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Article Details

On Some Properties of Space S_{w}^{α}

Authors: Erdem TOKSOY | Ayşe SANDIKÇI

Publisher: Erzincan Binali Yildirim University

Main Topics: Applied physics

Journal: Erzincan University Journal of Science and Technology 2020 Vol.13 Issue 2, pp.923-934

Document Type: Article

Publication Date: 8/2020

Document Language: Turkish

Document ID (Org No.): 2000414595

eISSN: 2149-4584

pISSN: 1307-9085

Issues

Authors:

Erdem TOKSOY | Ayşe SANDIKÇI

Publisher:

Erzincan Binali Yildirim University

Main Topics:

Applied physics

Journal:

Erzincan University Journal of Science and Technology 2020 Vol.13 Issue 2, pp.923-934

Document Type:

Article

Publication Date:

8/2020

Document Language:

Turkish

Document ID (Org No.):

2000414595

eISSN:

2149-4584

pISSN:

1307-9085