A note on semistable unitary operators on $L^2(\mathbb{R})$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908741670010880 |
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| author | Chen, Xianghong |
| author_facet | Chen, Xianghong |
| contents | In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under dilation. As a consequence, we characterize one-parameter groups formed by such operators, which are of the form $e^{iβt|{d}/{dx}|^α}$, with $α,β\in\mathbb R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_25013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on semistable unitary operators on $L^2(\mathbb{R})$ Chen, Xianghong Functional Analysis Mathematical Physics 47D03, 35Q41 In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under dilation. As a consequence, we characterize one-parameter groups formed by such operators, which are of the form $e^{iβt|{d}/{dx}|^α}$, with $α,β\in\mathbb R$. |
| title | A note on semistable unitary operators on $L^2(\mathbb{R})$ |
| topic | Functional Analysis Mathematical Physics 47D03, 35Q41 |
| url | https://arxiv.org/abs/2512.25013 |