Localization operators on discrete Orlicz modulation spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911372947750912 |
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| author | Dasgupta, Aparajita Poria, Anirudha |
| author_facet | Dasgupta, Aparajita Poria, Anirudha |
| contents | In this paper, we introduce Orlicz spaces on $ \mathbb Z^n \times \mathbb T^n $ and Orlicz modulation spaces on $\mathbb Z^n$, and present some basic properties such as inclusion relations, convolution relations, and duality of these spaces. We show that the Orlicz modulation space $M^Φ(\mathbb Z^n)$ is close to the modulation space $M^{2}(\mathbb Z^n)$ for some particular Young function $Φ$. Then, we study a class of pseudo-differential operators known as time-frequency localization operators on $\mathbb Z^n$, which depend on a symbol $ς$ and two windows functions $g_1$ and $g_2$. Using appropriate classes for symbols, we study the boundedness of the localization operators on Orlicz modulation spaces on $\mathbb Z^n$. Also, we show that these operators are compact and in the Schatten--von Neumann classes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_05373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localization operators on discrete Orlicz modulation spaces Dasgupta, Aparajita Poria, Anirudha Functional Analysis Primary 47G30, Secondary 42B35, 47B10 In this paper, we introduce Orlicz spaces on $ \mathbb Z^n \times \mathbb T^n $ and Orlicz modulation spaces on $\mathbb Z^n$, and present some basic properties such as inclusion relations, convolution relations, and duality of these spaces. We show that the Orlicz modulation space $M^Φ(\mathbb Z^n)$ is close to the modulation space $M^{2}(\mathbb Z^n)$ for some particular Young function $Φ$. Then, we study a class of pseudo-differential operators known as time-frequency localization operators on $\mathbb Z^n$, which depend on a symbol $ς$ and two windows functions $g_1$ and $g_2$. Using appropriate classes for symbols, we study the boundedness of the localization operators on Orlicz modulation spaces on $\mathbb Z^n$. Also, we show that these operators are compact and in the Schatten--von Neumann classes. |
| title | Localization operators on discrete Orlicz modulation spaces |
| topic | Functional Analysis Primary 47G30, Secondary 42B35, 47B10 |
| url | https://arxiv.org/abs/2409.05373 |