On Some Properties of Space $S^{a}_{w}$

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Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.13, no.2, pp.923-934, 2020 (Peer-Reviewed Journal) identifier


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 w f L  such that the fractional Fourier transform F f  belongs to ( ) d w S  . We endow this space with the sum norm 1, w w S w S 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 L w 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.