Heisenberg-Pauli-Weyl uncertainty principles for the fractional Dunkl transform on the real line
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913724494774272 |
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| author | Ghosh, Sunit Bhat, Younis Ahmad Swain, Jitendriya |
| author_facet | Ghosh, Sunit Bhat, Younis Ahmad Swain, Jitendriya |
| contents | The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty principle for the fractional Dunkl transform, with $1 \leq p \leq 2$. For the case $p = 2$, we further derive a sharper uncertainty principle for the fractional Dunkl transform. Furthermore, we derive conditions leading to equality in both the uncertainty principles obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heisenberg-Pauli-Weyl uncertainty principles for the fractional Dunkl transform on the real line Ghosh, Sunit Bhat, Younis Ahmad Swain, Jitendriya Functional Analysis Primary 44A15, 42A38, Secondary 94A12 The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty principle for the fractional Dunkl transform, with $1 \leq p \leq 2$. For the case $p = 2$, we further derive a sharper uncertainty principle for the fractional Dunkl transform. Furthermore, we derive conditions leading to equality in both the uncertainty principles obtained. |
| title | Heisenberg-Pauli-Weyl uncertainty principles for the fractional Dunkl transform on the real line |
| topic | Functional Analysis Primary 44A15, 42A38, Secondary 94A12 |
| url | https://arxiv.org/abs/2503.05409 |