A Note on Function Spaces with Fractional Fourier Transforms in Wiener-type Spaces
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 bec...
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| Format: | Article |
| Language: | English |
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Düzce University
2023-04-01
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| Series: | Düzce Üniversitesi Bilim ve Teknoloji Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/2231950 |
| Summary: | 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. |
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| ISSN: | 2148-2446 |