On Some Properties of Space w S

Yıl 2020, , 923 - 934, 31.08.2020

Erdem Toksoy , Ayşe Sandıkçı

https://doi.org/10.18185/erzifbed.635545

Cited By: 1

Öz

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

Anahtar Kelimeler

Fractional Fourier transform,, convolution, Segal algebras.

On Some Properties of Space S_{w}^{α}

Öz

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.

Anahtar Kelimeler

Fractional Fourier transform, convolution, Segal algebras

Kaynakça

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