On the iterates of the Laguerre operator
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917668797284352 |
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| author | Jakšić, Smiljana Pilipović, Stevan Teofanov, Nenad Vučković, Đorđe |
| author_facet | Jakšić, Smiljana Pilipović, Stevan Teofanov, Nenad Vučković, Đorđe |
| contents | We use the iterates of the Laguerre operator to introduce Pilipović spaces on positive orthants. It is shown that such spaces coincide with $G-$type spaces $g_α^α(\mathbb{R}^d_+)$ and $G_α^α(\mathbb{R}^d_+)$, when $α> 1$, and $α\geq 1$, respectively. However, in contrast to $G$-type spaces, Pilipović spaces on positive orthants are nontrivial below the critical index $α= 1$. We also remark that there is a natural isomorphism between subspaces of Pilipović spaces on $\mathbb{R}^d$ consisting of even functions, and Pilipović spaces on positive orthants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the iterates of the Laguerre operator Jakšić, Smiljana Pilipović, Stevan Teofanov, Nenad Vučković, Đorđe Functional Analysis 46F05, 33C45 We use the iterates of the Laguerre operator to introduce Pilipović spaces on positive orthants. It is shown that such spaces coincide with $G-$type spaces $g_α^α(\mathbb{R}^d_+)$ and $G_α^α(\mathbb{R}^d_+)$, when $α> 1$, and $α\geq 1$, respectively. However, in contrast to $G$-type spaces, Pilipović spaces on positive orthants are nontrivial below the critical index $α= 1$. We also remark that there is a natural isomorphism between subspaces of Pilipović spaces on $\mathbb{R}^d$ consisting of even functions, and Pilipović spaces on positive orthants. |
| title | On the iterates of the Laguerre operator |
| topic | Functional Analysis 46F05, 33C45 |
| url | https://arxiv.org/abs/2405.10694 |